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Surface groups acting on CAT(-1) spaces

Lookup NU author(s): Dr Alina Vdovina

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This is the authors' accepted manuscript of an article that has been published in its final definitive form by Cambridge University Press, 2019.

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Abstract

© Cambridge University Press, 2017 Harmonic map theory is used to show that a convex cocompact surface group action on a (Formula presented.) 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 (Formula presented.) space has Hausdorff dimension (Formula presented.), where the inequality is strict unless the action is Fuchsian.

Publication metadata

Author(s): Daskalipoulos G, Mese C, Sanders A, Vdovina A

Publication type: Article

Publication status: Published

Journal: Ergodic Theory and Dynamical Systems

Year: 2019

Volume: 39

Issue: 7

Pages: 1843-1856

Print publication date: 01/07/2019

Online publication date: 04/12/2017

Acceptance date: 10/08/2017

Date deposited: 16/01/2018

ISSN (print): 0143-3857

ISSN (electronic): 1469-4417

Publisher: Cambridge University Press

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

DOI: 10.1017/etds.2017.103

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