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
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
Views: 6216
Created: 30th Jan 2020 at 09:39
Last updated: 5th Mar 2024 at 21:24
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