Related papers: Exponential Mixing Via Additive Combinatorics

We prove the local mixing theorem for geodesic flows on abelian covers finite volume hyperbolic surfaces with cusps, which is a continuation of the work of Oh-Pan. We also describe applications to counting problems and the prime geodesic…

In the unit tangent bundle of noncompact finite volume negatively curved Riemannian manifolds, we prove the equidistribution towards the measure of maximal entropy for the geodesic flow of the Lebesgue measure along the divergent geodesic…

We study both function theoretic and spectral properties on complete noncompact smooth metric measure space $(M,g,e^{-f}dv)$ with nonnegative Bakry-\'{E}mery Ricci curvature. Among other things, we derive a gradient estimate for positive…

We construct geodesics in the Wasserstein space of probability measure along which all the measures have an upper bound on their density that is determined by the densities of the endpoints of the geodesic. Using these geodesics we show…

We study the asymptotic behaviour of simply connected, Riemannian manifolds $X$ of strictly negative curvature admitting a non-uniform lattice $\Gamma$. If the quotient manifold $\bar X= \Gamma \backslash X$ is asymptotically $1/4$-pinched,…

We consider a surface M with constant curvature cusp ends and its Eisenstein functions E_j(\lambda). These are the plane waves associated to the j-th cusp and the spectral parameter \lambda, (\Delta - 1/4 - \lambda^2)E_j = 0. We prove that…

If $(M,g)$ is a smooth compact rank $1$ Riemannian manifold without focal points, it is shown that the measure $\mu_{\max}$ of maximal entropy for the geodesic flow is unique. In this article, we study the statistic properties and prove…

We consider the inverse mean curvature flow in smooth Riemannian manifolds of the form $([R_{0},\infty)\times S^n,\bar{g})$ with metric $\bar{g}=dr^2+{\vartheta}^2(r){\sigma}$ and non-positive radial sectional curvature. We prove, that for…

We prove that if a geodesic metric measure space satisfies a comparison condition for isoperimetric profile and if the observable variance is maximal, then the space is foliated by minimal geodesics, where the observable variance is defined…

Let $X$ be a proper, geodesically complete CAT(0) space under a proper, non-elementary, isometric action by a group $\Gamma$ with a rank one element. We construct a generalized Bowen-Margulis measure on the space of unit-speed parametrized…

In this article we study geodesic flows on closed Riemannian manifolds without conjugate points and divergence property of geodesic rays. If the fundamental group is Gromov hyperbolic and residually finite we prove, under appropriate…

A theorem of Godefroy and Shapiro states that non-trivial convolution operators on the space of entire functions on $\mathbb{C}^n$ are hypercyclic. Moreover, it was shown by Bonilla and Grosse-Erdmann that they have frequently hypercyclic…

In this article, we establish the Hopf-Tsuji-Sullivan dichotomy for geodesic flows on certain manifolds with no conjugate points: either the geodesic flow is conservative and ergodic, or it is completely dissipative and non-ergodic. We also…

Let S be a nonexceptional oriented surface of finite type. We construct an uncountable family of probability measures on the space of area on holomorphic quadratic differentials over the moduli space for S containing the usual Lebesgue…

In this article we examine the concentration and oscillation effects developed by high-frequency eigenfunctions of the Laplace operator in a compact Riemannian manifold. More precisely, we are interested in the structure of the possible…

Let $(M,g)$ be a compact manifold without conjugate points and with visibility universal covering. We show that its geodesic flow has a time-preserving expansive factor which is topologically mixing and has a local product structure. As an…

Let $f$ be a $C^{1+\alpha}$ diffeomorphism of a compact manifold $M$ preserving a smooth measure $\mu$. We show that if $f:(M,\mu)\to (M,\mu)$ is exponentially mixing then it is Bernoulli.

This paper is devoted to the geometric analysis of the incompressible averaged Euler equations on compact Riemannian manifolds with boundary. The equation also coincides with the model for a second-grade non-Newtonian fluid. We study the…

A recent paper [CGT] studies the evolution of star-shaped mean convex hypersurfaces of the Euclidean space by a class of nonhomogeneous expanding curvature flows. In the present paper we consider the same problem in the real, complex and…

Let $f: [0,1]\times [0,1] \setminus {1/2} \to [0,1]\times [0,1]$ be the $C^\infty$ endomorphism given by $$f(x,y)=(2x- [2x], y+ c/|x-1/2|- [y+ c/|x-1/2|]),$$ where $c$ is a positive real number. We prove that $f$ is topologically mixing and…