Geometric finiteness in negatively pinched Hadamard manifolds

Geometric infiniteness in negatively pinched Hadamard manifolds

We generalize Bonahon's characterization of geometrically infinite torsion-free discrete subgroups of PSL(2, $\mathbb{C}$) to geometrically infinite discrete isometry subgroups in the case of rank 1 symmetric spaces, and, under the assumption of bounded torsion, to the case of negatively pinched Hadamard manifolds. Every such geometrically infinite isometry subgroup $Γ$ has a set of nonconical limit points with cardinality of continuum.

Hadamard流形的等距几何有限群的代数熵的非零性

Nonvanishing of algebraic entropy for geometrically finite groups of isometries of Hadamard manifolds

我们证明了捏挤Hadamard流形的任何几何有限（非初等）等距群都具有均匀的指数增长性。

Hadamard 流形中的乒乓论证

Ping-pong in Hadamard manifolds

本文针对负压缩 Hadamard 流形建立定量 Tits 二择一结果，证明两个非椭圆等距生成的非初等离散群含词长一致有界的秩 2 自由子群，并在双曲情形给出凸余紧性。

作用于双曲空间的群的漂移与联合极小位移

Drift and joint minimal displacement for groups acting on hyperbolic spaces

该研究针对作用于双曲空间的群，基于联合极小位移得到随机游走漂移的统一下界，其主定理适用于弱轴化作用，还在相关群的漂移谱中得到零处的统一间隙。

关于变负曲率的Mostow刚性

On Mostow rigidity for variable negative curvature

证明了一类具有收缩负截面曲率、基本群固定、维数为$>2$的完备有限体积黎曼流形的有限性定理。其中一个关键的成分是，这样一个流形的基本群不允许一个小的非平凡的作用在$R$树。

Equidistribution and counting of orbit points for discrete rank one isometry groups of Hadamard spaces

Let $X$ be a proper, geodesically complete Hadamard space, and $\ Γ<\mbox{Is}(X)$ a discrete subgroup of isometries of $X$ with the fixed point of a rank one isometry of $X$ in its infinite limit set. In this paper we prove that if $Γ$ has non-arithmetic length spectrum, then the Ricks' Bowen-Margulis measure -- which generalizes the well-known Bowen-Margulis measure in the CAT$(-1)$ setting -- is mixing. If in addition the Ricks' Bowen-Margulis measure is finite, then we also have equidistribution of $Γ$-orbit points in $X$, which in particular yields an asymptotic estimate for the orbit coun…