Surface groups acting on spaces
Keyword(s):
Harmonic map theory is used to show that a convex cocompact surface group action on a $\text{CAT}(-1)$ 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 $\text{CAT}(-1)$ space has Hausdorff dimension $\geq 1$, where the inequality is strict unless the action is Fuchsian.
2010 ◽
Vol 31
(6)
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pp. 1849-1864
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Keyword(s):
2002 ◽
Vol 65
(2)
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pp. 199-209
Keyword(s):
2019 ◽
Vol 2019
(746)
◽
pp. 149-170
Keyword(s):
1994 ◽
Vol 46
(2)
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pp. 298-307
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2011 ◽
Vol 139
(08)
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pp. 2767-2767
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2019 ◽
Vol 150
(5)
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pp. 2379-2386
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