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Authors:Chenkai Liu, Ran Zhuo Abstract: Communications in Contemporary Mathematics, Ahead of Print. In this paper, we study the weak strong uniqueness of the Dirichlet type problems of fractional Laplace (Poisson) equations. We construct the Green’s function and the Poisson kernel. We then provide a somewhat sharp condition for the solution to be unique. We also show that the solution under such condition exists and must be given by our Green’s function and Poisson kernel. In doing these, we establish several basic and useful properties of the Green’s function and Poisson kernel. Based on these, we obtain some further a priori estimates of the solutions. Surprisingly those estimates are quite different from the ones for the local type elliptic equations such as Laplace equations. These are basic properties to the fractional Laplace equations and can be useful in the study of related problems. Citation: Communications in Contemporary Mathematics PubDate: 2024-08-06T07:00:00Z DOI: 10.1142/S0219199724500378
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Authors:Yuxin Ge, Mingxiang Li, Zhao Lian Abstract: Communications in Contemporary Mathematics, Ahead of Print. In this work, we study a functional involving the generalized scalar curvatures and prove a spherical sphere theorem under some pinching condition of this quantity. As an application, we define a new invariant on [math]-dimensional manifolds and use it to study the topology of manifolds. Citation: Communications in Contemporary Mathematics PubDate: 2024-07-27T07:00:00Z DOI: 10.1142/S0219199724500366
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Authors:Yaozhong Qiu Abstract: Communications in Contemporary Mathematics, Ahead of Print. We show a symmetric Markov diffusion semigroup satisfies a weighted contractivity condition if and only if a [math]-Hardy inequality holds, and we give a Bakry–Émery-type criterion for the former. We then give some applications. Citation: Communications in Contemporary Mathematics PubDate: 2024-07-09T07:00:00Z DOI: 10.1142/S0219199724500238
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Authors:Simon Lentner, Karolina Vocke Abstract: Communications in Contemporary Mathematics, Ahead of Print. For a quantum group, we study those right coideal subalgebras, for which all irreducible representations are one-dimensional. If a right coideal subalgebra is maximal with this property, then we call it a Borel subalgebra. Besides the positive part of the quantum group and its reflections, we find new unfamiliar Borel subalgebras, for example, ones containing copies of the quantum Weyl algebra. Given a Borel subalgebra, we study its induced (Verma-)modules and prove among others that they have all irreducible finite-dimensional modules as quotients. We give two structural conjectures involving the associated graded right coideal subalgebra, which we prove in certain cases. In particular, they predict the shape of all triangular Borel subalgebras. As examples, we determine all Borel subalgebras of [math] and [math] and discuss the induced modules. Citation: Communications in Contemporary Mathematics PubDate: 2024-07-06T07:00:00Z DOI: 10.1142/S0219199724500287
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Authors:Michele Graffeo Abstract: Communications in Contemporary Mathematics, Ahead of Print. Let [math] be a representation of a finite abelian group and let [math] be the space of generic stability conditions on the set of [math]-constellations. We provide a combinatorial description of all the chambers [math] and prove that there are [math] of them. Moreover, we introduce the notion of simple chamber and we show that, in order to know all toric [math]-constellations, it is enough to build all simple chambers. We also prove that there are [math] simple chambers. Finally, we provide an explicit formula for the tautological bundles [math] over the moduli spaces [math] for all chambers [math] which only depends upon the chamber stair which is a combinatorial object attached to the chamber [math]. Citation: Communications in Contemporary Mathematics PubDate: 2024-06-26T07:00:00Z DOI: 10.1142/S0219199724500196
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Authors:M. van den Berg Abstract: Communications in Contemporary Mathematics, Ahead of Print. Upper bounds are obtained for the Newtonian capacity of compact sets in [math] in terms of the perimeter of the [math]-parallel neighborhood of [math]. For compact, convex sets in [math] with a [math] boundary the Newtonian capacity is bounded from above by [math], where [math] is the integral of the mean curvature over the boundary of [math] with equality if [math] is a ball. For compact, convex sets in [math] with non-empty interior the Newtonian capacity is bounded from above by [math] with equality if [math] is a ball. Here, [math] is the perimeter of [math] and [math] is its measure. A quantitative refinement of the latter inequality in terms of the Fraenkel asymmetry is also obtained. An upper bound is obtained for expected Newtonian capacity of the Wiener sausage in [math] with radius [math] and time length [math]. Citation: Communications in Contemporary Mathematics PubDate: 2024-06-19T07:00:00Z DOI: 10.1142/S0219199724500275
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Authors:Filip Broćić Abstract: Communications in Contemporary Mathematics, Ahead of Print. Given an open neighborhood [math] of the zero section in the cotangent bundle of [math] we define a distance-like function [math] on [math] using certain symplectic embeddings from the standard ball [math] to [math]. We show that when [math] is the unit-disk cotangent bundle of a Riemannian metric on [math], [math] recovers the metric. As an intermediate step, we give a new construction of a symplectic embedding of the ball of capacity 4 to the product of Lagrangian disks [math], and we give a new proof of the strong Viterbo conjecture about normalized capacities for [math]. We also give bounds of the symplectic packing number of two balls in a unit-disk cotangent bundle relative to the zero section [math]. Citation: Communications in Contemporary Mathematics PubDate: 2024-06-13T07:00:00Z DOI: 10.1142/S021919972450024X
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Authors:Francesca Da Lio, Ali Hyder Abstract: Communications in Contemporary Mathematics, Ahead of Print. In this paper, we study the asymptotic behavior of sequences of stationary weak solutions to the following Liouville-type equation: −Δu = euinΩ,(1) where [math] is an open set. By improving the partial regularity estimates obtained by the first author in F. Da Lio [Partial regularity for stationary solutions to Liouville-type equation in dimension 3, Comm. Partial Differential Equations 33(10–12) (2008) 1890–1910] for Eq. () we succeed in performing a blow-up analysis without Morrey-type assumptions on the solutions [math] and on the nonlinearity [math] Citation: Communications in Contemporary Mathematics PubDate: 2024-06-06T07:00:00Z DOI: 10.1142/S0219199724500202
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Authors:Serena Federico, Zongyuan Li, Xueying Yu Abstract: Communications in Contemporary Mathematics, Ahead of Print. In this paper, we prove unique continuation properties for linear variable coefficient Schrödinger equations with bounded real potentials. Under certain smallness conditions on the leading coefficients, we prove that solutions decaying faster than any cubic exponential rate at two different times must be identically zero. Assuming a transversally anisotropic type condition, we recover the sharp Gaussian (quadratic exponential) rate in the series of works by Escauriaza–Kenig–Ponce–Vega [On uniqueness properties of solutions of Schrödinger equations, Comm. Partial Differential Equations 31(10–12) (2006) 1811–1823; Hardy’s uncertainty principle, convexity and Schrödinger evolutions, J. Eur. Math. Soc. (JEMS) 10(4) (2008) 883–907; The sharp Hardy uncertainty principle for Schrödinger evolutions, Duke Math. J. 155(1) (2010) 163–187]. Citation: Communications in Contemporary Mathematics PubDate: 2024-05-29T07:00:00Z DOI: 10.1142/S0219199724500160
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Authors:Marco Capolli, Andrea Pinamonti, Gareth Speight Abstract: Communications in Contemporary Mathematics, Ahead of Print. We investigate the connection between maximal directional derivatives and differentiability for Lipschitz functions defined on Laakso space. We show that maximality of a directional derivative for a Lipschitz function implies differentiability only for a [math]-porous set of points. On the other hand, the distance to a fixed point is differentiable everywhere except for a [math]-porous set of points. This behavior is completely different to the previously studied settings of Euclidean spaces, Carnot groups and Banach spaces. Hence, the techniques used in these spaces do not generalize to metric measure spaces. Citation: Communications in Contemporary Mathematics PubDate: 2024-05-15T07:00:00Z DOI: 10.1142/S0219199724500172
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Authors:Dong Liu, Yufeng Pei, Limeng Xia, Kaiming Zhao Abstract: Communications in Contemporary Mathematics, Ahead of Print. In this paper, we present a determinant formula for a contravariant form on Verma modules over the [math] Bondi–Metzner–Sachs (BMS) superalgebra. This formula establishes a necessary and sufficient condition for the irreducibility of the Verma modules. We then introduce and characterize a class of simple smooth modules that generalize both Verma and Whittaker modules over the [math] BMS superalgebra. We also utilize the Heisenberg–Clifford vertex superalgebra to construct a free field realization for the [math] BMS superalgebra. This free field realization allows us to obtain a family of natural smooth modules over the [math] BMS superalgebra, which includes Fock modules and certain Whittaker modules. Citation: Communications in Contemporary Mathematics PubDate: 2024-05-10T07:00:00Z DOI: 10.1142/S0219199724500214
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Authors:Brian Weber Abstract: Communications in Contemporary Mathematics, Ahead of Print. This paper shows how a Levi-flat or pseudoconvex submanifold in a Kähler 4-manifold restricts the ambient manifold’s topology and its geometry at infinity. Citation: Communications in Contemporary Mathematics PubDate: 2024-05-07T07:00:00Z DOI: 10.1142/S0219199724500147
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Authors:Matthias Ostermann Abstract: Communications in Contemporary Mathematics, Ahead of Print. In this paper, we show that any Sobolev norm of nonnegative integer order of radially symmetric functions is equivalent to a weighted Sobolev norm of their radial profile. This establishes in terms of weighted Sobolev spaces on an interval a complete characterization of radial Sobolev spaces, which was open until now. As an application, we give a description of Sobolev norms of corotational maps. Citation: Communications in Contemporary Mathematics PubDate: 2024-05-07T07:00:00Z DOI: 10.1142/S0219199724500184
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Authors:Claudio Gorodski, Iryna Kashuba, María Eugenia Martin Abstract: Communications in Contemporary Mathematics, Ahead of Print. We study the variety of complex [math]-dimensional Jordan algebras using techniques from Geometric Invariant Theory. More specifically, we use the Kirwan–Ness theorem to construct a Morse-type stratification of the variety of Jordan algebras into finitely many invariant locally closed subsets, with respect to the energy functional associated to the canonical moment map. In particular we obtain a new, cohomology-free proof of the well-known rigidity of semisimple Jordan algebras in the context of the variety of Jordan algebras. Citation: Communications in Contemporary Mathematics PubDate: 2024-05-04T07:00:00Z DOI: 10.1142/S0219199724500159
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Authors:Ying Dong, Shuai Zhang Abstract: Communications in Contemporary Mathematics, Ahead of Print. The self-consistent chemotaxis-Navier–Stokes system with nonlinear diffusion ∂tn + u ⋅∇n = ∇⋅ (nm−1∇n) −∇⋅ (n∇c) + ∇⋅ (n∇ϕ), ∂tc + u ⋅∇c = Δc − nc, ∂tu + (u ⋅∇)u + ∇P = Δu − n∇ϕ + n∇c, ∇⋅u = 0 is considered in a bounded domain [math] with smooth boundary. Compared to the previously most-studied chemotaxis-fluid system proposed in [I. Tuval, L. Cisneros, C. Dombrowski, C. W. Wolgemuth, J. O. Kessler and R. E. Goldstein, Bacterial swimming and oxygen transport near contact lines, Proc. Natl. Acad. Sci. USA. 102 (2005) 2277–2282], the coupling in this system is stronger and more nonlinear. When the system is accompanied by homogeneous boundary conditions of no-flux type for [math] and [math], and of Dirichlet type for [math], a quasi-Lyapunov structure provides sufficient regularity features to facilitate a basic existence theory. However, if we change the boundary condition of the signal to c = c⋆(x,t),x ∈ ∂Ω, t> 0, with a given non-negative function [math][math], then the Dirichlet boundary condition imposed here seems to destroy the quasi-Lyapunov structure. Despite this, we shall find a new energy structure and prove that for suitably regular initial data, the assumption [math] is sufficient for the global existence and boundedness of the weak solution. To the best of our knowledge, this is the first work on the global well-posedness problem of the self-consistent chemotaxis-fluid system involving Dirichlet boundary conditions for the signal. Citation: Communications in Contemporary Mathematics PubDate: 2024-05-04T07:00:00Z DOI: 10.1142/S0219199724500226
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Authors:I. Alvarez-Romero, B. Barrios, J. J. Betancor Abstract: Communications in Contemporary Mathematics, Ahead of Print. In this paper, we consider the heat semigroup [math] defined by the combinatorial Laplacian and two subordinated families of [math] on homogeneous trees [math]. We characterize the weights [math] on [math] for which the pointwise convergence to initial data of the above families holds for every [math] with [math], where [math] represents the counting measure in [math]. We prove that this convergence property in [math] is equivalent to the fact that the maximal operator on [math], for some [math], defined by the semigroup is bounded from [math] into [math] for some weight [math] on [math]. Citation: Communications in Contemporary Mathematics PubDate: 2024-04-18T07:00:00Z DOI: 10.1142/S021919972450010X
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Authors:Xiangsheng Wang Abstract: Communications in Contemporary Mathematics, Ahead of Print. For the moduli space of the punctured spheres, we find a new equality between two symplectic forms defined on it. Namely, by treating the elements of this moduli space as the singular Euclidean metrics on a sphere, we give an interpretation of the complex hyperbolic form, i.e. the Kähler form of the complex hyperbolic structure on the moduli space, as a kind of Weil–Petersson form. Citation: Communications in Contemporary Mathematics PubDate: 2024-04-13T07:00:00Z DOI: 10.1142/S0219199724500068
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Authors:Lucia Bagnoli, Slaven Kožić Abstract: Communications in Contemporary Mathematics, Ahead of Print. We study the double Yangian associated with the Lie superalgebra [math]. Our main focus is on establishing the Poincaré–Birkhoff–Witt Theorem for the double Yangian and constructing its central elements in the form of coefficients of the quantum contraction. Next, as an application, we introduce reflection algebras, certain left coideal subalgebras of the level 0 double Yangian, and find their presentations by generators and relations. Citation: Communications in Contemporary Mathematics PubDate: 2024-04-13T07:00:00Z DOI: 10.1142/S021919972450007X
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Authors:Shangkun Weng, Zihao Zhang Abstract: Communications in Contemporary Mathematics, Ahead of Print. This paper concerns the structural stability of subsonic flows with a contact discontinuity in a finitely long axisymmetric cylinder. We establish the existence and uniqueness of axisymmetric subsonic flows with a contact discontinuity by prescribing the horizontal mass flux distribution, the swirl velocity, the entropy and the Bernoulli’s quantity at the entrance and the radial velocity at the exit. It can be formulated as a free boundary problem with the contact discontinuity to be determined simultaneously with the flows. Compared with the two-dimensional case, a new difficulty arises due to the singularity near the axis. An invertible modified Lagrangian transformation is introduced to overcome this difficulty and straighten the contact discontinuity. The key elements in our analysis are to utilize the deformation-curl decomposition introduced in [S. Weng and Z. Xin, A deformation-curl decomposition for three dimensional steady Euler equations, Sci. Sin. Math. 49 (2019) 307–320 (in Chinese): doi:10.1360/N012018-00125] to effectively decouple the hyperbolic and elliptic modes in the steady axisymmetric Euler system and to use the implicit function theorem to locate the contact discontinuity. Citation: Communications in Contemporary Mathematics PubDate: 2024-04-10T07:00:00Z DOI: 10.1142/S0219199724500081
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Authors:Antonio Alarcón, Ildefonso Castro-Infantes, Jorge Hidalgo Abstract: Communications in Contemporary Mathematics, Ahead of Print. We prove that every open Riemann surface [math] is the complex structure of a complete surface of constant mean curvature [math] ([math]) in the three-dimensional hyperbolic space [math]. We go further and establish a jet interpolation theorem for complete conformal [math] immersions [math]. As a consequence, we show the existence of complete densely immersed [math] surfaces in [math] with arbitrary complex structure. We obtain these results as application of a uniform approximation theorem with jet interpolation for holomorphic null curves in [math] which is also established in this paper. Citation: Communications in Contemporary Mathematics PubDate: 2024-04-10T07:00:00Z DOI: 10.1142/S0219199724500111
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Authors:Csaba Farkas, Sándor Kajántó, Alexandru Kristály Abstract: Communications in Contemporary Mathematics, Ahead of Print. The goal of this paper is to provide sharp spectral gap estimates for problems involving higher-order operators (including both the clamped and buckling plate problems) on Cartan–Hadamard manifolds. The proofs are symmetrization-free — thus no sharp isoperimetric inequality is needed — based on two general, yet elementary functional inequalities. The spectral gap estimate for clamped plates solves a sharp asymptotic problem from [Q.-M. Cheng and H. Yang, Universal inequalities for eigenvalues of a clamped plate problem on a hyperbolic space, Proc. Amer. Math. Soc. 139(2) (2011) 461–471] concerning the behavior of higher-order eigenvalues on hyperbolic spaces, and answers a question raised in [A. Kristály, Fundamental tones of clamped plates in nonpositively curved spaces, Adv. Math. 367(39) (2020) 107113] on the validity of such sharp estimates in high-dimensional Cartan–Hadamard manifolds. As a byproduct of the general functional inequalities, various Rellich inequalities are established in the same geometric setting. Citation: Communications in Contemporary Mathematics PubDate: 2024-04-10T07:00:00Z DOI: 10.1142/S0219199724500135
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Authors:Cristian Bereanu Abstract: Communications in Contemporary Mathematics, Ahead of Print. In this paper, we study the Lorentz force equation with the rest mass [math] and periodic boundary conditions on a fixed interval [math] q′ 1 − q′ 2′ = E(t,q) + q′× B(t,q),q(0) = q(T),q′(0) = q′(T), where [math] are the electric and magnetic fields. From the Poincaré paper concerning the special relativity it is well known that this is the Euler–Lagrange equation of the action functional given by ℐ∗(q) =∫0T[1 −1 − q′ 2 + q′⋅ W(t,q) − V (t,q)]dt, defined for all [math]-periodic Lipschitz functions [math] such that [math] In this paper, under some assumptions on the potentials [math] and [math] around zero and infinity, we prove that [math] has nonzero critical points which are [math]-periodic solutions of the Lorentz force equation. To prove our main results we use new “mountain pass” methods for the Poincaré action functional [math] Citation: Communications in Contemporary Mathematics PubDate: 2024-04-03T07:00:00Z DOI: 10.1142/S0219199724500093
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Authors:Lucas Backes, Davor Dragičević, Mihály Pituk Abstract: Communications in Contemporary Mathematics, Ahead of Print. It is known that hyperbolic nonautonomous linear delay differential equations in a finite dimensional space are Hyers–Ulam stable and hence shadowable. The converse result is available only in the special case of autonomous and periodic linear delay differential equations with a simple spectrum. In this paper, we prove the converse and hence the equivalence of all three notions in the title for a general class of nonautonomous linear delay differential equations with uniformly bounded coefficients. The importance of the boundedness assumption is shown by an example. Citation: Communications in Contemporary Mathematics PubDate: 2024-03-27T07:00:00Z DOI: 10.1142/S0219199724500123
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Authors:Luan Bezerra, Evgeny Mukhin Abstract: Communications in Contemporary Mathematics, Ahead of Print. We construct Fock and MacMahon modules for the quantum toroidal superalgebra [math] associated with the Lie superalgebra [math] and parity [math]. The bases of the Fock and MacMahon modules are labeled by super-analogs of partitions and plane partitions with various boundary conditions, while the action of generators of [math] is given by Pieri-type formulas. We study the corresponding characters. Citation: Communications in Contemporary Mathematics PubDate: 2024-03-09T08:00:00Z DOI: 10.1142/S0219199724500020
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Authors:Adam Czapliński, Andreas Krug, Manfred Lehn, Sönke Rollenske Abstract: Communications in Contemporary Mathematics, Ahead of Print. We observe that general reducible curves in sufficiently positive linear systems on K3 surfaces are of a form that generalize Kodaira’s classification of singular elliptic fibers and thus call them extended ADE curves. On such a curve [math], we describe a compactified Jacobian and show that its components reflect the intersection graph of [math]. This extends known results when [math] is reduced, but new difficulties arise when [math] is non-reduced. As an application, we get an explicit description of general singular fibers of certain Lagrangian fibrations of Beauville–Mukai type. Citation: Communications in Contemporary Mathematics PubDate: 2024-03-09T08:00:00Z DOI: 10.1142/S0219199724500044
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Authors:Wu-Hsiung Huang Abstract: Communications in Contemporary Mathematics, Ahead of Print. In this paper, we establish a “global” Morse index theorem. Given a hypersurface [math] of constant mean curvature, immersed in [math]. Consider a continuous deformation of “generalized” Lipschitz domain [math] enlarging in [math]. The topological type of [math] is permitted to change along [math], so that [math] has an arbitrary shape which can “reach afar” in [math], i.e. cover any preassigned area. The proof of the global Morse index theorem is reduced to the continuity in [math] of the Sobolev space [math] of variation functions on [math], as well as the continuity of eigenvalues of the stability operator. We devise a “detour” strategy by introducing a notion of “set-continuity” of [math] in [math] to yield the required continuities of [math] and of eigenvalues. The global Morse index theorem thus follows and provides a structural theorem of the existence of Jacobi fields on domains in [math]. Citation: Communications in Contemporary Mathematics PubDate: 2024-02-28T08:00:00Z DOI: 10.1142/S0219199723500645
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Authors:Vincenzo Ambrosio Abstract: Communications in Contemporary Mathematics, Ahead of Print. We consider the fractional relativistic Schrödinger–Choquard equation (−Δ + m2)su + V (ðœ€x)u = 1 x μ ∗ F(u) f(u)inℝN,u ∈ Hs(ℝN),u> 0inℝN, where [math] is a small parameter, [math], [math], [math], [math], [math] is the fractional relativistic Schrödinger operator, [math] is a continuous potential having a local minimum, [math] is a continuous nonlinearity with subcritical growth at infinity and [math]. Exploiting appropriate variational arguments, we construct a family of solutions concentrating around the local minimum of [math] as [math]. Citation: Communications in Contemporary Mathematics PubDate: 2024-02-23T08:00:00Z DOI: 10.1142/S021919972350061X
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Authors:Dražen Adamović, Kazuya Kawasetsu, David Ridout Abstract: Communications in Contemporary Mathematics, Ahead of Print. The Bershadsky–Polyakov algebras are the subregular quantum Hamiltonian reductions of the affine vertex operator algebras associated with [math]. In (D. Adamović, K. Kawasetsu and D. Ridout, A realisation of the Bershadsky–Polyakov algebras and their relaxed modules, Lett. Math. Phys. 111 (2021) 38, arXiv:2007.00396 [math.QA]), we realized these algebras in terms of the regular reduction, Zamolodchikov’s W3-algebra, and an isotropic lattice vertex operator algebra. We also proved that a natural construction of relaxed highest-weight Bershadsky–Polyakov modules has the property that the result is generically irreducible. Here, we prove that this construction, when combined with spectral flow twists, gives a complete set of irreducible weight modules whose weight spaces are finite-dimensional. This gives a simple independent proof of the main classification theorem of (Z. Fehily, K. Kawasetsu and D. Ridout, Classifying relaxed highest-weight modules for admissible-level Bershadsky–Polyakov algebras, Comm. Math. Phys. 385 (2021) 859–904, arXiv:2007.03917 [math.RT]) for nondegenerate admissible levels and extends this classification to a category of weight modules. We also deduce the classification for the nonadmissible level [math], which is new. Citation: Communications in Contemporary Mathematics PubDate: 2024-02-23T08:00:00Z DOI: 10.1142/S0219199723500633
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Authors:Brian Grajales, Lino Grama, Rafaela F. Prado Abstract: Communications in Contemporary Mathematics, Ahead of Print. In this paper, we examine the geodesics on adjoint orbits of [math] that are equipped with [math]-invariant metrics, where [math] is the maximal compact subgroup. Our primary technique involves translating this problem into a geometric problem in the tangent bundle of certain [math]-flag manifolds and describing the geodesic equations with respect to the Sasaki metric on the tangent bundle. Additionally, we utilize tools from Lie Theory to obtain explicit descriptions of families of geodesics. We provide a detailed analysis of the case for [math]. Citation: Communications in Contemporary Mathematics PubDate: 2024-02-23T08:00:00Z DOI: 10.1142/S0219199724500019
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Authors:Fulin Chen, Haisheng Li, Shaobin Tan Abstract: Communications in Contemporary Mathematics, Ahead of Print. In this paper, we study nullity-[math] toroidal extended affine Lie algebras in the context of vertex algebras and their [math]-coordinated modules. Among the main results, we introduce a variant of toroidal extended affine Lie algebras, associate vertex algebras to the variant Lie algebras, and establish a canonical connection between modules for toroidal extended affine Lie algebras and [math]-coordinated modules for these vertex algebras. Furthermore, by employing some results of Billig, we obtain an explicit realization of a class of irreducible modules for the variant Lie algebras. Citation: Communications in Contemporary Mathematics PubDate: 2024-02-23T08:00:00Z DOI: 10.1142/S0219199724500032
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Authors:Luis M. Briceño-Arias, Patrick L. Combettes, Francisco J. Silva Abstract: Communications in Contemporary Mathematics, Ahead of Print. The classical perspective of a function is a construction which transforms a convex function into one that is jointly convex with respect to an auxiliary scaling variable. Motivated by applications in several areas of applied analysis, we investigate an extension of this construct in which the scaling variable is replaced by a nonlinear term. Our construction is placed in the general context of locally convex spaces and it generates a lower semicontinuous convex function under broad assumptions on the underlying functions. Various convex-analytical properties are established and closed-form expressions are derived. Several applications are presented. Citation: Communications in Contemporary Mathematics PubDate: 2024-02-19T08:00:00Z DOI: 10.1142/S0219199723500657
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Authors:Amin Esfahani, Achenef Tesfahun Abstract: Communications in Contemporary Mathematics, Ahead of Print. In this paper, the sixth-order Boussinesq equation is studied. We extend the local well-posedness theory for this equation with quadratic and cubic nonlinearities to the high dimensional case. In spite of having the “bad” fourth term [math] in the equation, we derive some dispersive estimates leading to the existence of local solutions which also improves the previous results in the cubic case. In addition, we show persistence of spatial analyticity of solutions for the cubic nonlinearity. Citation: Communications in Contemporary Mathematics PubDate: 2024-02-16T08:00:00Z DOI: 10.1142/S0219199724500056
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Authors:Veronica Felli, Ana Primo, Giovanni Siclari Abstract: Communications in Contemporary Mathematics, Ahead of Print. A classification of local asymptotic profiles and strong unique continuation properties are established for a class of fractional heat equations with a Hardy-type potential, via an Almgren–Poon monotonicity formula combined with a blow-up analysis. Citation: Communications in Contemporary Mathematics PubDate: 2024-02-14T08:00:00Z DOI: 10.1142/S0219199723500621
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Authors:Eric Larson Abstract: Communications in Contemporary Mathematics, Ahead of Print. Let [math] be a general Brill–Noether curve. A classical problem is to determine when [math], which controls the quadric section of [math]. So far this problem has only been solved in characteristic zero, in which case [math] with finitely many exceptions. In this paper, we extend these results to positive characteristic, uncovering a wealth of new exceptions in characteristic [math]. Citation: Communications in Contemporary Mathematics PubDate: 2024-02-14T08:00:00Z DOI: 10.1142/S0219199723500670
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Authors:Gianmarco Giovannardi, Manuel Ritoré Abstract: Communications in Contemporary Mathematics, Ahead of Print. In the Heisenberg group [math] with a sub-Finsler structure, an [math]-Lipschitz surface which is complete, oriented, connected and stable must be a vertical plane. In particular, the result holds for entire intrinsic graphs of Euclidean Lipschitz functions. Citation: Communications in Contemporary Mathematics PubDate: 2024-02-09T08:00:00Z DOI: 10.1142/S0219199723500487
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Authors:Andrea Santi, Dennis The Abstract: Communications in Contemporary Mathematics, Ahead of Print. For the largest exceptional simple Lie superalgebra [math], having dimension [math], we provide two explicit geometric realizations as supersymmetries, namely as the symmetry superalgebra of super-PDE systems of second- and third-order, respectively. Citation: Communications in Contemporary Mathematics PubDate: 2024-02-01T08:00:00Z DOI: 10.1142/S0219199723500530
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Authors:Marcin Bilski, Jacek Bochnak, Wojciech Kucharz Abstract: Communications in Contemporary Mathematics, Ahead of Print. Let [math] be an uncountable field of characteristic [math]. For a given function [math], with [math], we prove that [math] is regular if and only if the restriction [math] is a regular function for every algebraic curve [math] in [math] which is either an affine line or is isomorphic to a plane curve in [math] defined by the equation [math], where [math] are prime numbers. We also show that regularity of [math] can be verified on other algebraic curves in [math] with desired geometric properties. Furthermore, if the field [math] is not algebraically closed, we construct a [math]-valued function on [math] that is not regular, but all its restrictions to nonsingular algebraic curves in [math] are regular functions. Citation: Communications in Contemporary Mathematics PubDate: 2024-01-29T08:00:00Z DOI: 10.1142/S0219199723500669
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Authors:Inkang Kim, Xueyuan Wan, Genkai Zhang Abstract: Communications in Contemporary Mathematics, Ahead of Print. We study Kähler metrics on the total space of Griffiths negative holomorphic vector bundles over Kähler manifolds. As an application, we construct mapping class group invariant Kähler metrics on [math], the holomorphic tangent bundle of Teichmüller space of a closed surface [math]. Consequently,we obtain a new mapping class group invariant Kähler metric on the quasi-Fuchsian space [math], which extends the Weil–Petersson metric on the Teichmüller space [math]. We also calculate its curvature and prove non-positivity for the curvature along the tautological directions. Citation: Communications in Contemporary Mathematics PubDate: 2024-01-24T08:00:00Z DOI: 10.1142/S0219199723500591
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Authors:Luigi Montoro, Berardino Sciunzi, Alessandro Trombetta Abstract: Communications in Contemporary Mathematics, Ahead of Print. In this paper, we prove a comparison principle for sub-supersolutions to a singular quasilinear problem that involves the anisotropic Finsler operator −ΔpHu := −div(Hp−1(∇u)∇H(∇u)). As a main consequence, we obtain a uniqueness result for weak solutions to the problem (℘). The proof is carried out also proving a sharp regularity result of the solutions up to the boundary. Our results are new even in the euclidean case. Citation: Communications in Contemporary Mathematics PubDate: 2024-01-24T08:00:00Z DOI: 10.1142/S0219199723500608
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Authors:Nikolaos Panagiotis Souris Abstract: Communications in Contemporary Mathematics, Ahead of Print. We study the relation between two special classes of Riemannian Lie groups [math] with a left-invariant metric [math]: The Einstein Lie groups, defined by the condition [math], and the geodesic orbit Lie groups, defined by the property that any geodesic is the integral curve of a Killing vector field. The main results imply that extensive classes of compact simple Einstein Lie groups [math] are not geodesic orbit manifolds, thus providing large-scale answers to a relevant question of Nikonorov. Our approach involves studying and characterizing the [math]-invariant geodesic orbit metrics on Lie groups [math] for a wide class of subgroups [math] that we call (weakly) regular. By-products of our work are structural and characterization results that are of independent interest for the classification problem of geodesic orbit manifolds. Citation: Communications in Contemporary Mathematics PubDate: 2024-01-24T08:00:00Z DOI: 10.1142/S0219199723500682
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