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June 2015 Rigidity for quasi-Möbius actions on fractal metric spaces
Kyle Kinneberg
J. Differential Geom. 100(2): 349-388 (June 2015). DOI: 10.4310/jdg/1430744124

Abstract

In Rigidity for quasi-Möbius group actions, M. Bonk and B. Kleiner proved a rigidity theorem for expanding quasi-Möbius 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 $\textrm{CAT}(-1)$-spaces that can be seen as a metric analog to the “entropy rigidity” theorems of U. Hamenstädt and M. Bourdon. Building on the ideas developed in Rigidity for quasi-Möbius group actions, we establish a rigidity theorem for certain expanding quasi-Möbius 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. "Rigidity for quasi-Möbius actions on fractal metric spaces." J. Differential Geom. 100 (2) 349 - 388, June 2015. https://doi.org/10.4310/jdg/1430744124

Information

Published: June 2015
First available in Project Euclid: 4 May 2015

zbMATH: 1328.53052
MathSciNet: MR3343835
Digital Object Identifier: 10.4310/jdg/1430744124

Rights: Copyright © 2015 Lehigh University

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Vol.100 • No. 2 • June 2015
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