Subjects -> MATHEMATICS (Total: 1013 journals)     - APPLIED MATHEMATICS (92 journals)    - GEOMETRY AND TOPOLOGY (23 journals)    - MATHEMATICS (714 journals)    - MATHEMATICS (GENERAL) (45 journals)    - NUMERICAL ANALYSIS (26 journals)    - PROBABILITIES AND MATH STATISTICS (113 journals) MATHEMATICS (GENERAL) (45 journals)
 Showing 1 - 35 of 35 Journals sorted alphabetically Acta Universitatis Sapientiae, Mathematica Algebra Letters       (Followers: 1) American Journal of Computational Mathematics       (Followers: 4) American Journal of Mathematics and Statistics       (Followers: 8) Annals of Global Analysis and Geometry       (Followers: 2) Archiv der Mathematik Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry       (Followers: 1) Bulletin of the American Mathematical Society       (Followers: 5) Communications in Mathematics Communications in Mathematics and Statistics       (Followers: 3) Conformal Geometry and Dynamics Difficoltà in Matematica Ergodic Theory and Dynamical Systems       (Followers: 3) International Journal of Applied Metaheuristic Computing       (Followers: 2) International Journal of Computing Science and Mathematics       (Followers: 1) International Journal of Mathematics and Statistics       (Followers: 2) Journal of Elliptic and Parabolic Equations Journal of Mathematical Physics       (Followers: 25) Journal of Physics A : Mathematical and Theoretical       (Followers: 22) Journal of the American Mathematical Society AMS       (Followers: 6) Jurnal Fourier       (Followers: 1) Mathematical Journal of Interdisciplinary Sciences       (Followers: 1) Mathematical Programming       (Followers: 14) Mathematics       (Followers: 3) Mathematics of Computation       (Followers: 5) Mathematika Memoirs of the American Mathematical Society AMS       (Followers: 2) Optimization: A Journal of Mathematical Programming and Operations Research       (Followers: 6) Pesquimat Pro Mathematica Proceedings of the American Mathematical Society AMS       (Followers: 4) Representation Theory       (Followers: 1) St. Petersburg Mathematical Journal       (Followers: 1) Theoretical Mathematics & Applications Transactions of the Moscow Mathematical Society       (Followers: 1)
Similar Journals
 Annals of Global Analysis and GeometryJournal Prestige (SJR): 1.228 Citation Impact (citeScore): 1Number of Followers: 2      Hybrid journal (It can contain Open Access articles) ISSN (Print) 1572-9060 - ISSN (Online) 0232-704X Published by Springer-Verlag  [2467 journals]
• On the Steklov spectrum of covering spaces and total spaces

Abstract: Abstract We show the existence of a natural Dirichlet-to-Neumann map on Riemannian manifolds with boundary and bounded geometry, such that the bottom of the Dirichlet spectrum is positive. This map regarded as a densely defined operator in the $$L^2$$ -space of the boundary admits Friedrichs extension. We focus on the spectrum of this operator on covering spaces and total spaces of Riemannian principal bundles over compact manifolds.
PubDate: 2023-01-17

• Delorme’s intertwining conditions for sections of homogeneous vector
bundles on two- and three-dimensional hyperbolic spaces

Abstract: Abstract The description of the Paley–Wiener space for compactly supported smooth functions $$C^\infty _c(G)$$ on a semi-simple Lie group G involves certain intertwining conditions that are difficult to handle. In the present paper, we make them completely explicit for $$G=\textbf{SL}(2,\mathbb {R})^d$$ ( $$d\in \mathbb {N}$$ ) and $$G=\textbf{SL}(2,\mathbb {C})$$ . Our results are based on a defining criterion for the Paley–Wiener space, valid for general groups of real rank one, that we derive from Delorme’s proof of the Paley–Wiener theorem. In a forthcoming paper, we will show how these results can be used to study solvability of invariant differential operators between sections of homogeneous vector bundles over the corresponding symmetric spaces.
PubDate: 2022-12-05

• On the eigenforms of compact stratified spaces

Abstract: Abstract Let X be a compact Thom–Mather stratified pseudomanifold, and let M be the regular part of X endowed with an iterated metric. In this paper, we prove that if the curvature operator of M is bounded, then the $$L^2$$ harmonic space of M is finite dimensional. Next we consider the absolute eigenvalue problems of the Hodge Laplacian of a sequence of compact domains $$\Omega _j$$ converging to M. We prove that when the curvature operator of M is bounded, the eigenvalues of $$\Omega _j$$ converge to eigenvalues of M, and the eigenforms of $$\Omega _j$$ converge to eigenforms of M in the Sobolev norm. This generalizes Chavel and Feldman’s theorem in Chavel and Feldman (J Funct Anal 30:198-222, 1978) from compact manifolds to compact pseudomanifolds and from functions to differential forms. Then, we apply our results to $$L^2$$ -chomology. We will give a correspondence between boundary cohomology and $$L^2$$ -cohomology.
PubDate: 2022-11-24

• The effect of pinching conditions in prescribing $$Q$$ -curvature on
standard spheres

Abstract: Abstract In this paper, we study the problem of prescribing a fourth-order conformal invariant on standard spheres. This problem is variational but it is noncompact due to the presence of nonconverging orbits of the gradient flow, the so called critical points at infinity. Following the method advised by Bahri we determine all such critical points at infinity and compute their contribution to the difference of topology between the level sets of the associated Euler–Lagrange functional. We then derive some existence results under pinching conditions.
PubDate: 2022-11-07
DOI: 10.1007/s10455-022-09878-6

• Complexes, residues and obstructions for log-symplectic manifolds

Abstract: Abstract We consider compact Kählerian manifolds X of even dimension 4 or more, endowed with a log-symplectic structure $$\Phi$$ , a generically nondegenerate closed 2-form with simple poles on a divisor D with local normal crossings. A simple linear inequality involving the iterated Poincaré residues of $$\Phi$$ at components of the double locus of D ensures that the pair $$(X, \Phi )$$ has unobstructed deformations and that D deforms locally trivially.
PubDate: 2022-11-07
DOI: 10.1007/s10455-022-09881-x

• Compact geodesic orbit spaces with a simple isotropy group

Abstract: Abstract Let $$M=G/H$$ be a compact, simply connected, Riemannian homogeneous space, where G is (almost) effective and H is a simple Lie group. In this paper, we first classify all G-naturally reductive metrics on M, and then all G-geodesic orbit metrics on M.
PubDate: 2022-11-07
DOI: 10.1007/s10455-022-09877-7

• Higher-power harmonic maps and sections

Abstract: Abstract The variational theory of higher-power energy is developed for mappings between Riemannian manifolds, and more generally sections of submersions of Riemannian manifolds, and applied to sections of Riemannian vector bundles and their sphere subbundles. A complete classification is then given for left-invariant vector fields on three-dimensional unimodular Lie groups equipped with an arbitrary left-invariant Riemannian metric.
PubDate: 2022-11-07
DOI: 10.1007/s10455-022-09875-9

• Umehara algebra and complex submanifolds of indefinite complex space forms

Abstract: Abstract The Umehara algebra is studied with motivation on the problem of the non-existence of common complex submanifolds. In this paper, we prove some new results in Umehara algebra and obtain some applications. In particular, if a complex manifolds admits a holomorphic polynomial isometric immersion to one indefinite complex space form, then it cannot admits a holomorphic isometric immersion to another indefinite complex space form of different type. Other consequences include the non-existence of the common complex submanifolds for indefinite complex projective space or hyperbolic space and a complex manifold with a distinguished metric, such as homogeneous domains, the Hartogs triangle, the minimal ball, and the symmetrized polydisc, equipped with their intrinsic Bergman metrics, which generalizes more or less all existing results.
PubDate: 2022-10-27
DOI: 10.1007/s10455-022-09876-8

• Nonexistence and rigidity of spacelike mean curvature flow solitons
immersed in a GRW spacetime

Abstract: Abstract We study the nonexistence and rigidity of an important class of particular cases of trapped submanifolds, more precisely, n-dimensional spacelike mean curvature flow solitons related to the closed conformal timelike vector field $$\mathcal K=f(t)\partial _t$$ ( $$t\in I\subset \mathbb R$$ ) which is globally defined on an $$(n+p+1)$$ -dimensional generalized Robertson–Walker (GRW) spacetime $$-I\times _fM^{n+p}$$ with warping function $$f\in C^\infty (I)$$ and Riemannian fiber $$M^{n+p}$$ , via applications of suitable generalized maximum principles and under certain constraints on f and on the curvatures of $$M^{n+p}$$ . In codimension 1, we also obtain new Calabi–Bernstein-type results concerning the spacelike mean curvature flow soliton equation in a GRW spacetime.
PubDate: 2022-10-24
DOI: 10.1007/s10455-022-09879-5

• First $$\frac{2}{n}$$ -stability eigenvalue of singular minimal
hypersurfaces in space forms

Abstract: Abstract In this paper, we study the first $$\frac{2}{n}$$ -stability eigenvalue on singular minimal hypersurfaces in space forms. We provide a characterization of catenoids in space forms in terms of $$\frac{2}{n}$$ -stable eigenvalue. We emphasize that this result is even new in the regular setting.
PubDate: 2022-10-21
DOI: 10.1007/s10455-022-09880-y

• p-Kähler and balanced structures on nilmanifolds with nilpotent
complex structures

Abstract: Abstract Let (X, J) be a nilmanifold with an invariant nilpotent complex structure. We study the existence of p-Kähler structures (which include Kähler and balanced metrics) on X. More precisely, we determine an optimal p such that there are no p-Kähler structures on X. Finally, we show that, contrarily to the Kähler case, on compact complex manifolds there is no relation between the existence of balanced metrics and the degeneracy step of the Frölicher spectral sequence. More precisely, on balanced manifolds the degeneracy step can be arbitrarily large.
PubDate: 2022-09-24
DOI: 10.1007/s10455-022-09867-9

• Nonhomogeneous expanding flows in hyperbolic spaces

Abstract: Abstract In the present paper, we consider star-shaped mean convex hypersurfaces of the real, complex and quaternionic hyperbolic space evolving by a class of nonhomogeneous expanding flows. For any choice of the ambient manifold, the initial conditions are preserved and the long-time existence of the flow is proved. The geometry of the ambient space influences the asymptotic behaviour of the flow: after a suitable rescaling, the induced metric converges to a conformal multiple of the standard Riemannian round metric of the sphere if the ambient manifold is the real hyperbolic space; otherwise, it converges to a conformal multiple of the standard sub-Riemannian metric on the odd-dimensional sphere. Finally, in every case, we are able to construct infinitely many examples such that the limit does not have constant scalar curvature.
PubDate: 2022-09-09
DOI: 10.1007/s10455-022-09873-x

• On triangulations of orbifolds and formality

Abstract: Abstract For an orbifold, there are two naturally associated differential graded algebras, one is the de Rham algebra of orbifold differential forms and the other one is the differential graded algebra of piecewise polynomial differential forms of a triangulation of the coarse space. In this paper, we prove that these two differential graded algebras are weakly equivalent; hence, the formality of these two differential graded algebras is consistent, when the triangulation is smooth. We show that global quotient orbifolds and global homogeneous isotropy orbifolds admit smooth triangulations; hence, the two kinds of formality coincide with each other for these orbifolds.
PubDate: 2022-09-08
DOI: 10.1007/s10455-022-09874-w

• On the second variation of the biharmonic Clifford torus in $$\mathbb S^4$$ S 4

Abstract: Abstract The flat torus $${{\mathbb T}}=\mathbb S^1\left( \frac{1}{2} \right) \times \mathbb S^1\left( \frac{1}{2} \right)$$ admits a proper biharmonic isometric immersion into the unit 4-dimensional sphere $$\mathbb S^4$$ given by $$\Phi =i \circ \varphi$$ , where $$\varphi :{{\mathbb T}}\rightarrow \mathbb S^3(\frac{1}{\sqrt{2}})$$ is the minimal Clifford torus and $$i:\mathbb S^3(\frac{1}{\sqrt{2}}) \rightarrow \mathbb S^4$$ is the biharmonic small hypersphere. The first goal of this paper is to compute the biharmonic index and nullity of the proper biharmonic immersion $$\Phi$$ . After, we shall study in the detail the kernel of the generalised Jacobi operator $$I_2^\Phi$$ . We shall prove that it contains a direction which admits a natural variation with vanishing first, second and third derivatives, and such that the fourth derivative is negative. In the second part of the paper, we shall analyse the specific contribution of $$\varphi$$ to the biharmonic index and nullity of $$\Phi$$ . In this context, we shall study a more general composition $${\tilde{\Phi }}=i \circ {\tilde{\varphi }}$$ , where $${\tilde{\varphi }}: M^m \rightarrow \mathbb S^{n-1}(\frac{1}{\sqrt{2}})$$ , $$m \ge 1$$ , $$n \ge {3}$$ , is a minimal immersion and $$i:\mathbb S^{n-1}(\frac{1}{\sqrt{2}}) \rightarrow \mathbb S^n$$ is the biharmonic small hypersphere. First, we shall determine a general sufficient condition which ensures that the second variation of $${\tilde{\Phi }}$$ is nonnegatively defined on $$\mathcal {C}\big ({\tilde{\varphi }}^{-1}T\mathbb S^{n-1}(\frac{1}{\sqrt{2}})\big )$$ . Then, we complete this type of analysis on our Clifford torus and, as a complementary result, we obtain the p-harmonic index and nullity of $$\varphi$$ . In the final section, we compare our general results with those which can be deduced from the study of the equivariant second variation.
PubDate: 2022-09-02
DOI: 10.1007/s10455-022-09869-7

• First integrals for Finsler metrics with vanishing $$\chi$$ χ
-curvature

Abstract: Abstract We prove that in a Finsler manifold with vanishing $$\chi$$ -curvature (in particular with constant flag curvature) some non-Riemannian geometric structures are geodesically invariant and hence they induce a set of non-Riemannian first integrals. Two alternative expressions of these first integrals can be obtained either in terms of the mean Berwald curvature, or as functions of the mean Cartan torsion and the mean Landsberg curvature.
PubDate: 2022-09-02
DOI: 10.1007/s10455-022-09872-y

• Graded hypoellipticity of BGG sequences

Abstract: Abstract This article studies hypoellipticity on general filtered manifolds. We extend the Rockland criterion to a pseudodifferential calculus on filtered manifolds, construct a parametrix and describe its precise analytic structure. We use this result to study Rockland sequences, a notion generalizing elliptic sequences to filtered manifolds. The main application that we present is to the analysis of the Bernstein–Gelfand–Gelfand (BGG) sequences over regular parabolic geometries. We do this by generalizing the BGG machinery to more general filtered manifolds (in a non-canonical way) and show that the generalized BGG sequences are Rockland in a graded sense.
PubDate: 2022-09-02
DOI: 10.1007/s10455-022-09870-0

• Constructions of helicoidal minimal surfaces and minimal annuli in
$$\widetilde{E(2)}$$ E ( 2 ) ~

Abstract: Abstract In this article, we construct two one-parameter families of properly embedded minimal surfaces in a three-dimensional Lie group $$\widetilde{E(2)}$$ , which is the universal covering of the group of rigid motions of Euclidean plane endowed with a left-invariant Riemannian metric. The first one can be seen as a family of helicoids, while the second one is a family of catenoidal minimal surfaces. The main tool that we use for the construction of these surfaces is a Weierstrass-type representation introduced by Meeks, Mira, Pérez and Ros for minimal surfaces in Lie groups of dimension three. In the end, we study the limit of the catenoidal minimal surfaces. As an application of this limit case, we get a new proof of a half-space theorem for minimal surfaces in $$\widetilde{E(2)}$$ .
PubDate: 2022-08-23
DOI: 10.1007/s10455-022-09871-z

• Special metrics and scales in parabolic geometry

Abstract: Abstract Given a parabolic geometry, it is sometimes possible to find special metrics characterised by some invariant conditions. In conformal geometry, for example, one asks for an Einstein metric in the conformal class. Einstein metrics have the special property that their geodesics are distinguished, as unparameterised curves, in the sense of parabolic geometry. This property characterises the Einstein metrics. In this article, we initiate a study of corresponding phenomena for other parabolic geometries, in particular for the hypersurface CR and contact Legendrean cases.
PubDate: 2022-07-28
DOI: 10.1007/s10455-022-09866-w

• Pullback functors for reduced and unreduced $$L^{q,p}$$ L q , p
-cohomology

Abstract: Abstract In this paper we study the reduced and unreduced $$L^{q,p}$$ -cohomology groups of oriented manifolds of bounded geometry and their behavior under uniform maps. A uniform map is a uniformly continuous map such that the diameter of the preimage of a subset is bounded in terms of the diameter of the subset itself. In general, for each $$p,q \in [1, +\infty )$$ , the pullback map along a uniform map does not induce a morphism between the spaces of p-integrable forms or even in $$L^{q,p}$$ -cohomology. Then our goal is to introduce, for each p in $$[1, +\infty )$$ and for each uniform map f between manifolds of bounded geometry, an $${\mathcal {L}}^p$$ -bounded operator $$T_f$$ , such that it does induce in a functorial way the appropriate morphism in reduced and unreduced $$L^{q,p}$$ -cohomology.
PubDate: 2022-07-11
DOI: 10.1007/s10455-022-09859-9

• A note on the moduli spaces of holomorphic and logarithmic connections
over a compact Riemann surface

Abstract: Abstract Let X be a compact Riemann surface of genus $$g \ge 3$$ . We consider the moduli space of holomorphic connections over X and the moduli space of logarithmic connections singular over a finite subset of X with fixed residues. We determine the Chow group of these moduli spaces. We compute the global sections of the sheaves of differential operators on ample line bundles and their symmetric powers over these moduli spaces and show that they are constant under certain conditions. We show the Torelli-type theorem for the moduli space of logarithmic connections. We also describe the rational connectedness of these moduli spaces.
PubDate: 2022-07-11
DOI: 10.1007/s10455-022-09864-y

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