Abstract: The article existence criteria for special locally conformally Kähler metrics, written by Nicolina Istrati, was originally published electronically on the publisher’s internet portal (currently SpringerLink) on July 14, 2018, with open access. PubDate: 2019-04-01

Abstract: Abstract We relate the operad \({\textit{FMan}}\) controlling the algebraic structure on the tangent sheaf of an F-manifold (weak Frobenius manifold) defined by Hertling and Manin to the operad \({\textit{PreLie}}\) of pre-Lie algebras: for the filtration of \({\textit{PreLie}}\) by powers of the ideal generated by the Lie bracket, the associated graded object is \({\textit{FMan}}\) . PubDate: 2019-04-01

Abstract: Abstract In this paper, we generalize the definition of the quaternionic Monge–Ampère operator to some unbounded plurisubharmonic functions, and we prove that the quaternionic Monge–Ampère operator is continuous on the monotonically decreasing sequences of plurisubharmonic functions. After introducing the generalized Lelong number of a positive current, Demailly’s comparison theorems are showed. Moreover, we prove that the quaternionic Lelong–Jensen-type formula also holds for the unbounded plurisubharmonic function. PubDate: 2019-04-01

Abstract: Abstract We introduce a CR-invariant class of Lorentzian metrics on a circle bundle over a three-dimensional CR structure, which we call FRT metrics. These metrics generalise the Fefferman metric, allowing for more control of the Ricci curvature, but are more special than the shearfree Lorentzian metrics introduced by Robinson and Trautman.Our main result is a criterion for embeddability of three-dimensional CR structures in terms of the Ricci curvature of the FRT metrics in the spirit of the results by Lewandowski et al. (Class Quantum Gravity 7(11):L241–L246, 1990) and also Hill et al. (Indiana Univ Math J 57(7):3131–3176, 2008. https://doi.org/10.1512/iumj.2008.57.3473). PubDate: 2019-04-01

Abstract: Abstract We prove embeddings of Sobolev and Hardy–Sobolev spaces into Besov spaces built upon certain mixed norms. This gives an improvement of the known embeddings into usual Besov spaces. Applying these results, we obtain Oberlin-type estimates of Fourier transforms for functions in Sobolev spaces \(W_1^1(\mathbb {R}^n).\) PubDate: 2019-04-01

Abstract: Abstract We prove local Hölder continuity of quasi-n-harmonic mappings from Euclidean domains into metric spaces with non-positive curvature in the sense of Alexandrov. We also obtain global Hölder continuity of such mappings from bounded Lipschitz domains. PubDate: 2019-04-01

Abstract: Abstract We investigate the relation between holomorphic torus actions on complex manifolds of locally conformally Kähler (LCK) type and the existence of special LCK metrics. We show that if the group of biholomorphisms of such a manifold (M, J) contains a compact torus which is not totally real, then there exists a Vaisman metric on the manifold, generalising a result of Kamishima–Ornea. Also, we obtain a new obstruction to the existence of LCK structures on a given complex manifold in terms of its automorphism group. As an application, we obtain a classification of manifolds of LCK type among all the manifolds having the structure of a holomorphic principal torus bundle. Moreover, we show that if the group of biholomorphisms contains a compact torus whose dimension is half the real dimension of M, then (M, J) admits an LCK metric with positive potential. Finally, we obtain new non-existence results for LCK metrics on certain products of complex manifolds. PubDate: 2019-04-01

Abstract: Abstract We study the backward invariant set of one-parameter semigroups of holomorphic self-maps of the unit disc. Such a set is foliated in maximal invariant curves, and its open connected components are petals, which are, in fact, images of Poggi-Corradini’s type pre-models. Hyperbolic petals are in one-to-one correspondence with repelling fixed points, while only parabolic semigroups can have parabolic petals. Petals have locally connected boundaries, and except a very particular case, they are indeed Jordan domains. The boundary of a petal contains the Denjoy–Wolff point, and except such a fixed point, the closure of a petal contains either no other boundary fixed points or a unique repelling fixed point. We also describe petals in terms of geometric and analytic behavior of Koenigs functions using divergence rate and universality of models. Moreover, we construct a semigroup having a repelling fixed point in such a way that the intertwining map of the pre-model is not regular. PubDate: 2019-04-01

Abstract: Abstract This paper deals with the general concept of chain recurrence for semigroup actions in the special case of flag bundles. An algebraic description of the maximal chain transitive sets is presented in terms of singularities of one-parameter subgroups in the flag manifolds. This description yields a generalization of the Selgrade theorem for semigroup actions on projective bundles. PubDate: 2019-04-01

Abstract: Abstract In this paper, we investigate sufficient conditions on the structure of the eigenspaces of a given finite family of matrices to assure the existence of an embedded pair of invariant multicones, which are the smallest and the biggest in a suitable and natural sense. Multicones, very similar structures to those known in the literature as 1-multicones, are quite natural generalizations of the classical cones. The conditions we find also suggest us a practical computational procedure for the actual construction of such invariant embedded pair. PubDate: 2019-04-01

Abstract: Abstract Results of Bernstein type are proven for supersolutions of the singular minimal surface equation when \(\alpha <0\) . In particular the non-existence of “entire” minimal graphs in hyperbolic space is shown. In addition we construct a foliation of \(\mathbb {R}^n\times \mathbb {R}^+\) consisting of minimizing surfaces, and solve a Dirichlet problem for the singular minimal surface equation. PubDate: 2019-04-01

Abstract: Abstract The present paper concerns the invariants of generically nef vector bundles on ruled surfaces. By Mehta–Ramanathan Restriction Theorem and by Miyaoka characterization of semistable vector bundles on a curve, the generic nefness can be considered as a weak form of semistability. We establish a Bogomolov-type inequality for generically nef vector bundles with nef general fiber restriction on ruled surfaces with no negative section, see Theorem 3.1. This gives an affirmative answer in this case to a problem posed by Peternell [17]. Concerning ruled surfaces with a negative section, we prove a similar result for generically nef vector bundles, with nef and balanced general fiber restriction and with a numerical condition on first Chern class, which is satisfied, for instance, if in its class there is a reduced divisor, see Theorem 3.5. Finally, we use such results to bound the invariants of curve fibrations, which factor through finite covers of ruled surfaces. PubDate: 2019-04-01

Abstract: Abstract Suppose that G and A are finite groups such that A acts coprimely on G via automorphisms. It is interesting to investigate the structure and properties of G when we impose some restrictions on its maximal A-invariant subgroups. More precisely, we prove the solvability of G when certain maximal A-invariant subgroups are nilpotent, when all maximal A-invariant subgroups are supersolvable, or when certain arithmetic conditions are imposed on non-nilpotent maximal A-invariant subgroups. PubDate: 2019-04-01

Abstract: Abstract This paper examines the global regularity problem of the two-dimensional Oldroyd-B-type model. When the initial \(L^2\) -energy is suitably small or the initial stress tensor is nonnegative definite, we show that the corresponding system admits a unique global regular solution. PubDate: 2019-04-01

Abstract: Abstract In this paper, we study biharmonic Riemannian submersions. We first derive bitension field of a general Riemannian submersion, and we then use it to obtain biharmonic equations for Riemannian submersions with one-dimensional fibers and Riemannian submersions with basic mean curvature vector fields of fibers. These are used to construct examples of proper biharmonic Riemannian submersions with one-dimensional fibers and to characterize warped products whose projections onto the first factor are biharmonic Riemannian submersions. PubDate: 2019-04-01

Abstract: Abstract Let M be complex projective manifold and A a positive line bundle on it. Assume that a compact and connected Lie group G acts on M in a Hamiltonian manner and that this action linearizes to A. Then, there is an associated unitary representation of G on the associated algebro-geometric Hardy space. If the moment map is nowhere vanishing, the isotypical components are all finite dimensional; they are generally not spaces of sections of some power of A. One is then led to study the local and global asymptotic properties the isotypical component associated with a weight \(k \, \varvec{ \nu }\) , when \(k\rightarrow +\infty \) . In this paper, part of a series dedicated to this general theme, we consider the case \(G=U(2)\) . PubDate: 2019-04-01

Abstract: Abstract In Masur (Ann Math 115(1):169–200, 1982) and Veech (J Anal Math 33:222–272, 1978), it was proved independently that almost every interval exchange transformation is uniquely ergodic. The Birkhoff ergodic theorem implies that these maps mainly have uniformly distributed orbits. This raises the question under which conditions the orbits yield low-discrepancy sequences. The case of \(n=2\) intervals corresponds to circle rotation, where conditions for low-discrepancy are well-known. In this paper, we give corresponding conditions in the case \(n=3\) . Furthermore, we construct infinitely many interval exchange transformations with low-discrepancy orbits for \(n \ge 4\) . We also show that these examples do not coincide with LS-sequences if \(S \ge 2\) . PubDate: 2019-04-01

Abstract: Abstract We develop a novel approach to study the global behaviour of large foodwebs for ecosystems where several species share multiple resources. The model extends and generalizes some previous works and takes into account self-limitation. Under certain explicit conditions, we establish the global convergence and persistence of solutions. PubDate: 2019-03-14

Abstract: Abstract The principle of optimizing inequalities, or their equivalent operator theoretic formulation, is well established in analysis. For an operator, this corresponds to extending its action to larger domains, hopefully to the largest possible such domain (i.e., its optimal domain). Some classical operators are already optimally defined (e.g., the Hilbert transform in \(L^p(\mathbb {R})\) , \(1<p<\infty \) ), and others are not (e.g., the Hausdorff–Young inequality in \(L^p(\mathbb {T})\) , \(1<p<2\) , or the Sobolev inequality in various spaces). In this paper, a detailed investigation is undertaken of the finite Hilbert transform T acting on rearrangement invariant spaces X on \((-1,1)\) , an operator whose singular kernel is neither positive nor does it possess any monotonicity properties. For a large class of such spaces X, it is shown that T is already optimally defined on X (this is known for \(L^p(-1,1)\) for all \(1<p<\infty \) , except \(p=2\) ). The case \(p=2\) is significantly different because the range of T is a proper dense subspace of \(L^2(-1,1)\) . Nevertheless, by a completely different approach, it is established that T is also optimally defined on \(L^2(-1,1)\) . Our methods are also used to show that the solution of the airfoil equation, which is well known for the spaces \(L^p(-1,1)\) whenever \(p\not =2\) (due to certain properties of T), can also be extended to the class of r.i. spaces X considered in this paper. PubDate: 2019-02-28

Abstract: Abstract We consider the Dirichlet problem for the nonhomogeneous equation \(-\Delta _p u -\Delta _q u = \alpha u ^{p-2}u + \beta u ^{q-2}u + f(x)\) in a bounded domain, where \(p \ne q\) , and \(\alpha , \beta \in \mathbb {R}\) are parameters. We explore assumptions on \(\alpha \) and \(\beta \) that guarantee the resolvability of the considered problem. Moreover, we introduce several curves on the \((\alpha ,\beta )\) -plane allocating sets of parameters for which the problem has or does not have positive or sign-changing solutions, provided f is of a constant sign. PubDate: 2019-02-19