格罗莫夫双曲空间的边界刚性

Pub Date : 2024-09-06 DOI:10.1007/s10711-024-00947-7
Hao Liang, Qingshan Zhou
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引用次数: 0

摘要

我们引入了格罗莫夫双曲空间边界刚性的概念。我们证明,当且仅当 Gromov 边界均匀完美时,具有极点的适当大地测量 Gromov 双曲空间是边界刚性的。作为应用,我们证明了对于非紧凑的格罗莫夫双曲完全黎曼流形或格罗莫夫双曲均匀图,边界刚性等同于具有正的切格等周常数,也等同于不可门。此外,当且仅当度量空间均匀完美时,紧凑度量空间的几种双曲填充被证明是边界刚性的。此外,边界刚性还被证明等同于大地丰富性,这是 Shchur 提出的概念(J Funct Anal 264(3):815-836, 2013)。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Boundary rigidity of Gromov hyperbolic spaces

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Boundary rigidity of Gromov hyperbolic spaces

We introduce the concept of boundary rigidity for Gromov hyperbolic spaces. We show that a proper geodesic Gromov hyperbolic space with a pole is boundary rigid if and only if its Gromov boundary is uniformly perfect. As an application, we show that for a non-compact Gromov hyperbolic complete Riemannian manifold or a Gromov hyperbolic uniform graph, boundary rigidity is equivalent to having positive Cheeger isoperimetric constant and also to being nonamenable. Moreover, several hyperbolic fillings of compact metric spaces are proved to be boundary rigid if and only if the metric spaces are uniformly perfect. Also, boundary rigidity is shown to be equivalent to being geodesically rich, a concept introduced by Shchur (J Funct Anal 264(3):815–836, 2013).

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