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

Hadamard 空间等距群的 $L^p$-上同调

$L^p$-cohomology for groups of isometries of Hadamard spaces

本文研究 Hadamard 流形等距作用与 $L^p$-上同调的联系，证明非初等作用可诱导非平凡的一阶 $L^p$-上同调。

Asymptotic Geometry in the product of Hadamard spaces with rank one isometries

In this article we study asymptotic properties of certain discrete groups $Γ$ acting by isometries on a product $\XX=\XX_1\times \XX_2$ of locally compact Hadamard spaces. The motivation comes from the fact that Kac-Moody groups over finite fields, which can be seen as generalizations of arithmetic groups over function fields, belong to this class of groups. Hence one may ask whether classical properties of discrete subgroups of higher rank Lie groups as in [MR1437472] and [MR1933790] hold in this context. In the first part of the paper we describe the structure of the geometric limit set of $…

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。

Generalized Patterson-Sullivan measures for products of Hadamard spaces

Let $Γ$ be a discrete group acting by isometries on a product $X=X_1\times X_2$ of Hadamard spaces. We further require that $X_1$, $X_2$ are locally compact and $Γ$ contains two elements projecting to a pair of independent rank one isometries in each factor. Apart from discrete groups acting by isometries on a product of CAT(-1)-spaces, the probably most interesting examples of such groups are Kac-Moody groups over finite fields acting on the Davis complex of their associated twin building. In a previous article we showed that the regular geometric limit set $\Lim$ splits as a product $F_Γ\tim…

Geometric finiteness in negatively pinched Hadamard manifolds

In this paper, we generalize Bonahon's characterization of geometrically infinite torsion-free discrete subgroups of PSL(2, $\mathbb{C}$) to geometrically infinite discrete subgroups $Γ$ of isometries of negatively pinched Hadamard manifolds $X$. We then generalize a theorem of Bishop to prove that every discrete geometrically infinite isometry subgroup $Γ$ has a set of nonconical limit points with the cardinality of the continuum.

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…