%0 Journal Article
%T Rigidity for Quasi-M£¿bius Actions on Fractal Metric Spaces
%A Kyle Kinneberg
%J Mathematics
%D 2013
%I arXiv
%X In \cite{BK02}, M. Bonk and B. Kleiner proved a rigidity theorem for expanding quasi-M\"obius group actions on Ahlfors $n$-regular metric spaces with topological dimension $n$. This led naturally to a rigidity result for quasi-convex geometric actions on $\CAT(-1)$-spaces that can be seen as a metric analog to the "entropy rigidity" theorems of U. Hamenst\"adt and M. Bourdon. Building on the ideas developed in \cite{BK02}, we establish a rigidity theorem for certain expanding quasi-M\"obius group actions on spaces with different metric and topological dimensions. This is motivated by a corresponding entropy rigidity result in the coarse geometric setting.
%U http://arxiv.org/abs/1308.0639v1