论文标题
猫（0）空间和teichmüller空间中均方根的摩尔斯指示的通用性
Genericity of sublinearly Morse directions in CAT(0) spaces and the Teichmüller space
论文作者
论文摘要
我们表明，在几种经常研究的单词感官中，在帕特森·苏利文（Patterson-Sullivan）的几种常见感官中，具有几何群体动作的cAT（0）空间的视觉边界的摩尔斯摩尔斯（Morse）方向是一般的。我们推断出，金属摩尔斯的边界是泊松边界的模型，用于在rank-1 cat（0）空间上作用于几何的组上有限支撑的随机步行。我们证明了在Teichmüller空间上映射类组动作的类似结果。我们的主要技术工具是一个标准，在任何独特的测量指标空间中有效，它说任何具有足够多（从统计意义上）强烈收缩的段的地理射线都可以均匀地签约。
We show that the sublinearly Morse directions in the visual boundary of a rank-1 CAT(0) space with a geometric group action are generic in several commonly studied senses of the word, namely with respect to Patterson-Sullivan measures and stationary measures for random walks. We deduce that the sublinearly Morse boundary is a model of the Poisson boundary for finitely supported random walks on groups acting geometrically on rank-1 CAT (0) spaces. We prove an analogous result for mapping class group actions on Teichmüller space. Our main technical tool is a criterion, valid in any unique geodesic metric space, that says that any geodesic ray with sufficiently many (in a statistical sense) strongly contracting segments is sublinearly contracting.
