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Lookup NU author(s): Dr Alina Vdovina
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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© 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.
Author(s): Daskalipoulos G, Mese C, Sanders A, Vdovina A
Publication type: Article
Publication status: Published
Journal: Ergodic Theory and Dynamical Systems
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
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