Related papers: Contraction property on complex hyperbolic ball
We study partially hyperbolic diffeomorphisms satisfying a trapping property which makes them look as if they were Anosov at large scale. We show that, as expected, they share several properties with Anosov diffeomorphisms. We construct an…
We prove rigidity results involving the Hawking mass for surfaces immersed in a $3$-dimensional, complete Riemannian manifold $(M,g)$ with non-negative scalar curvature (resp. with scalar curvature bounded below by $-6$). Roughly, the main…
We prove an Hopf-Lax-Oleinik formula for the solutions of some Hamilton- Jacobi equations on a general metric space. As a first consequence, we show in full gener- ality that the log-Sobolev inequality is equivalent to an hypercontractivity…
In this paper, we investigate the properties of hyperbolic harmonic mappings in the unit ball $\mathbb{B}^{n}$ in $\IR^n$ $(n\geq 2)$. Firstly, we establish necessary and sufficient conditions for a hyperbolic harmonic mapping to be in the…
We study the Hardy identities and inequalities on Cartan-Hadamard manifolds using the notion of a Bessel pair. These Hardy identities offer significantly more information on the existence/nonexistence of the extremal functions of the Hardy…
We generalize techniques by Coskun, Riedl, and Yeong, and obtain an almost optimal bound on the degree for the algebraic hyperbolicity of very general hypersurfaces in rational homogeneous varieties. As examples, we work out the cases of…
In thius paper we introduce the Hardy and Bergman spaces on hyperconvex domains relative to a acontinuous exhaustion function. We prove their basic properties and study their composition operators induced by holomorphic mappings between…
This paper continues a geometric study of Harvey's Complex of Curves, whose ultimate goal is to apply the theory of hyperbolic spaces and groups to algorithmic questions for the Mapping Class Group and geometric properties of Kleinian…
We start to develop the quantization formalism in a hyperbolic Hilbert space. Generalizing Born's probability interpretation, we found that unitary transformations in such a Hilbert space represent a new class of transformations of…
We state and prove a combination theorem for relatively hyperbolic groups seen as geometrically finite convergence groups. For that, we explain how to contruct a boundary for a group that is an acylindrical amalgamation of relatively…
Well-posedness of the initial (boundary) value problem is an essential property, both of meaningful physical models and of numerical applications. To prove well-posedness of wave-type equations their level of hyperbolicity is an essential…
It is shown that generalized trigonometric functions and generalized hyperbolic functions can be transformed from each other. As an application of this transformation, a number of properties for one immediately lead to the corresponding…
We give estimates on asymptotic dimensions of products of general hyperbolic spaces with following applications to the hyperbolic groups. We give examples of strict inequality in the product theorem for the asymptotic dimension in the class…
We define metrics in space that are natural counterparts of the hyperbolic metric in plane domains, using the characterization of the hyperbolic metric due to Beardon and Pommerenke. We obtain inequalities for these metrics under…
We study curvature-adapted submanifolds of general symmetric spaces. We generalize Cartan's theorem for isoparametric hypersurfaces of spheres and Wang's classification of isoparametric Hopf hypersurfaces in complex projective spaces to any…
We prove that for certain partially hyperbolic skew-products, non-uniform hyperbolicity along the leaves implies existence of a finite number of ergodic absolutely continuous invariant probability measures which describe the asymptotics of…
In this article we study a coarse version of the K-theoretic Farrell-Jones conjecture we call coarse or bounded isomorphism conjecture. With techniques that have already been used to prove the Farrell-Jones conjecture for hyperbolic groups…
We prove that for certain sequences of hyperbolic three--manifolds with cusps which converge to hyperbolic three--space in a weak ("Benjamini-Schramm") sense and certain coefficient systems the regularized analytic torsion approximates the…
We prove topological regularity results for isoperimetric sets in PI spaces having a suitable deformation property, which prescribes a control on the increment of the perimeter of sets under perturbations with balls. More precisely, we…
In this note we present various extensions of Obata's rigidity theorem concerning the Hessian of a function on a Riemannian manifold. They include general rigidity theorems for the generalized Obata equation, and hyperbolic and Euclidean…