Surface groups acting on CAT (-1) spaces

Abstract:

Harmonic map theory is used to show that a convex cocompact surface group action on a \mathrmCAT(-1) metric space fixes a convex copy of the hyperbolic plane (i.e. the action is Fuchsian) if and only if the Hausdorff dimension of the limit set of the action is equal to 1. This provides another proof of a result of Bonk and Kleiner. More generally, we show that the limit set of every convex cocompact surface group action on a \mathrmCAT(-1) space has Hausdorff dimension ≥1, where the inequality is strict unless the action is Fuchsian.

SEEK ID: https://publications.h-its.org/publications/961

DOI: 10.1017/etds.2017.103

Research Groups: Groups and Geometry

Publication type: Journal

Journal: Ergodic Theory Dynam. Systems

Citation: Ergod. Th. Dynam. Sys. 39(7):1843-1856

Date Published: 1st Jul 2019

URL: https://doi.org/10.1017/etds.2017.103

Registered Mode: imported from a bibtex file

Authors: GEORGIOS DASKALOPOULOS, CHIKAKO MESE, ANDREW SANDERS, ALINA VDOVINA

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Citation
DASKALOPOULOS, G. E. O. R. G. I. O. S., MESE, C. H. I. K. A. K. O., SANDERS, A. N. D. R. E. W., & VDOVINA, A. L. I. N. A. (2017). Surface groups acting on spaces. In Ergodic Theory and Dynamical Systems (Vol. 39, Issue 7, pp. 1843–1856). Cambridge University Press (CUP). https://doi.org/10.1017/etds.2017.103
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Created: 30th Jan 2020 at 09:39

Last updated: 5th Mar 2024 at 21:24

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