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We consider hyperbolic and partially hyperbolic diffeomorphisms on compact manifolds. Associated with invariant foliation of these systems, we define some topological invariants and show certain relationships between these topological…

Dynamical Systems · Mathematics 2007-05-23 Radu Saghin , Zhihong Xia

We prove a persistence result for noncompact normally hyperbolic invariant manifolds in Riemannian manifolds of bounded geometry. The bounded geometry of the ambient manifold is a crucial assumption in order to control the uniformity of all…

Dynamical Systems · Mathematics 2012-08-07 Jaap Eldering

Let $\Omega$ be a bounded, convex domain in a separable Hilbert space. The authors prove a version of the theorem of Bun Wong, which asserts that if such a domain admits an automorphism orbit accumulating at a strongly pseudoconvex boundary…

Complex Variables · Mathematics 2007-05-23 Kang-Tae Kim , Steven G. Krantz

We produce an equality between the Gromov-Witten invariants of the moduli space M of rank two odd degree stable vector bundles over a Riemann surface $\Sigma$ and the Donaldson invariants of the algebraic surface $\Sigma \times P^1$. We…

Algebraic Geometry · Mathematics 2007-05-23 Vicente Muñoz

Baseilhac-Benedetti, following ideas of Kashaev, introduced invariants of pseudo-Anosov homeomorphisms of punctured hyperbolic surfaces that depend on a complex root of unity of odd order. Around the same time, Bonahon-Liu introduced…

Geometric Topology · Mathematics 2026-01-08 Stavros Garoufalidis , Tao Yu

For compact Riemannian manifolds with convex boundary, B.White proved the following alternative: Either there is an isoperimetric inequality for minimal hypersurfaces or there exists a closed minimal hypersurface, possibly with a small…

Differential Geometry · Mathematics 2012-10-19 Victor Bangert , Nena Roettgen

We use Molecular Dynamics combined with Dissipative Particle Dynamics to construct a model of a binary mixture where the two species differ only in their dynamic properties (friction coefficients). For an asymmetric mixture of slow and fast…

Soft Condensed Matter · Physics 2009-11-11 Jacqueline Yaneva , Burkhard Duenweg , Andrey Milchev

We consider in this work a one parameter family of hypoelliptic diffusion processes on the unit tangent bundle $T^1 \mathcal M$ of a Riemannian manifold $(\mathcal M,g)$, collectively called kinetic Brownian motions, that are random…

Probability · Mathematics 2015-01-16 Jürgen Angst , Ismaël Bailleul , Camille Tardif

The results of this paper build upon those first obtained by Sznitman and Zeitouni in [11]. We establish, for spacial dimensions greater than two, the existence of a unique invariant measure for isotropic diffusions in random environment…

Analysis of PDEs · Mathematics 2014-04-22 Benjamin J. Fehrman

The construction of invariants of three-dimensional manifolds with a triangulated boundary, proposed earlier by the author for the case when the boundary consists of not more than one connected component, is generalized to any number of…

Geometric Topology · Mathematics 2011-06-02 Igor Korepanov

On a n-dimensional connected compact manifold with non-empty boundary equipped with a Riemannian metric, a spin structure and a chirality operator, we study some properties of a spin conformal invariant defined from the first eigenvalue of…

Differential Geometry · Mathematics 2009-03-10 Simon Raulot

We prove that if a holomorphic self-map $f\colon \Omega\to \Omega$ of a bounded strongly convex domain $\Omega\subset \mathbb C^q$ with smooth boundary is hyperbolic then it admits a natural semi-conjugacy with a hyperbolic automorphism of…

Complex Variables · Mathematics 2021-12-22 Amedeo Altavilla , Leandro Arosio , Lorenzo Guerini

We construct an unbounded strictly pseudoconvex Kobayashi hyperbolic and complete domain in $\mathbb{C}^2$, which also possesses complete Bergman metric, but has no nonconstant bounded holomorphic functions.

Complex Variables · Mathematics 2020-03-17 Nikolay Shcherbina , Liyou Zhang

We introduce an invariant of Riemannian geometry which measures the relative position of two von Neumann algebras in Hilbert space, and which, when combined with the spectrum of the Dirac operator, gives a complete invariant of Riemannian…

High Energy Physics - Theory · Physics 2011-04-28 Alain Connes

We study the geometry of fanning curves in the Grassmann manifold of n-dimensional subspaces of $\mathbb{R}^{kn}$; we construct a complete system of invariants which solve the congruence problem. The geometry of the invariants themselves…

Differential Geometry · Mathematics 2016-10-25 Carlos E. Durán , Cíntia R. de A. Peixoto

We give a group cohomological description of the \v{C}ech cohomology of the Bowditch boundary of a relatively hyperbolic group pair, generalizing a result of Bestvina-Mess about hyperbolic groups. In case of a relatively hyperbolic…

Group Theory · Mathematics 2020-09-01 Jason Fox Manning , Oliver Wang

We prove 3-dimensional hyperbolic cone-manifolds are geometrically inflexible: a cone-deformation of a hyperbolic cone-manifold determines a bi-Lipschitz diffeomorphism between initial and terminal manifolds in the deformation in the…

Geometric Topology · Mathematics 2014-12-16 Jeffrey Brock , Kenneth Bromberg

Let $M$ be a complex manifold with boundary $X$, which admits a holomorphic Lie group $G$-action preserving $X$. We establish a full asymptotic expansion for the $G$-invariant Bergman kernel under certain assumptions. As an application, we…

Complex Variables · Mathematics 2024-04-25 Chin-Yu Hsiao , Rung-Tzung Huang , Xiaoshan Li , Guokuan Shao

We first show that for a bounded pseudoconvex domain with a manifold quotient of finite-volume in the sense of Kahler-Einstein measure, the identity component of the automorphism group of this domain is semi-simple without compact factors.…

Differential Geometry · Mathematics 2018-09-07 Kefeng Liu , Yunhui Wu

In this thesis we talk about lipschitz-homotopy invariants for manifolds of bounded geometry. There are three main results: the first one is the definition of a controvariant functor between the category of manifolds of bounded geometry…

Differential Geometry · Mathematics 2021-09-16 Stefano Spessato