Boundaries of hyperbolic metric spaces
Boundaries of hyperbolic metric spaces
复制标题
双曲度量空间的边界
DOI：
--
复制
发表时间：
2003
期刊：
影响因子：
--
通讯作者：
A. Winchester
中科院分区：
文献类型：
--
作者：
Corran Webster;A. Winchester
研究了双曲度量空间的度量边界与Gromov边界之间的关系。我们证明了Gromov边界是度量边界的商，并且商映射是连续的，因此字双曲群在其Cayley图的度量边界上具有从属作用。此外，如果空间是0-双曲的，则边界是一致的，因此在这种空间的边界上不存在非Busemann点。这些结果对群C-代数上的Lip-范数的研究具有重要意义。
We investigate the relationship between the metric boundary and the Gromov boundary of a hyperbolic metric space. We show that the Gromov boundary is a quotient of the metric boundary and the quotient map is continuous, and that therefore a word-hyperbolic group has an amenable action on the metric boundary of its Cayley graph. Furthermore, if the space is 0-hyperbolic, the boundaries agree, and as a consequence there are no non-Busemann points on the boundary of such spaces. These results have significance for the study of Lip-norms on group C -algebras.