Uniform Cantor sets as hyperbolic boundaries
Uniform Cantor sets as hyperbolic boundaries
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DOI：
10.2298/fil1408737x
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发表时间：
2014
期刊：
影响因子：
0.8
通讯作者：
Yingqing Xiao;Junping Gu
中科院分区：
文献类型：
--
作者：
Yingqing Xiao;Junping Gu
本文证明了由Z. Simanyi等人在ZIJS是渐近PT-1空间的基础上，将ZIJS的方法推广到一致Cantor集的情形，证明了一致Cantor集等距于某个渐近PT-1空间的双曲边界.
In this paper, we prove that the Gromov hyperbolic space $(\mathcal{X}, h)$ which was introduced by Z. Ibragimov and J. Simanyi in \cite{ZIJS} is an asymptotically $\mathrm{PT}_{-1}$ space and extend the methods of \cite{ZIJS} to the case of uniform Cantor sets, show that the uniform Cantor set is isometric to the hyperbolic boundary of some asymptotically $\mathrm{PT}_{-1}$ space.