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arXiv · 1308.0639

Rigidity for Quasi-M\"obius Actions on Fractal Metric Spaces

Kyle Kinneberg
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Abstract

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.

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Kyle Kinneberg. 2013-08-02. Rigidity for Quasi-M\"obius Actions on Fractal Metric Spaces. https://arxiv.org/abs/1308.0639

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