论文标题
格罗莫夫双曲空间的边界刚度
Boundary rigidity of Gromov hyperbolic spaces
论文作者
论文摘要
我们介绍了Gromov双曲空间的边界刚性概念。我们表明，当且仅当其Gromov边界均匀地完美时，一个正确的地球Gromov双曲线空间是边界刚性的。作为一种应用，我们表明，对于非紧凑型Gromov双曲线完整的Riemannian歧管或Gromov双曲线均匀图，边界刚性等同于具有正cheeger等等等级常数，并且也与不可动作。此外，仅当公制空间均匀完美时，几个紧凑型公制空间的双曲线填充物被证明是刚性的。同样，边界刚度被证明等同于地球上的富含，这是Shchur引入的概念（J.Funct。Anal。，2013）。
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., 2013).
