The conformal measures of a normal subgroup of a cocompact Fuchsian group
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Abstract In this paper we study the conformal measures of a normal subgroup of a cocompact Fuchsian group. In particular, we relate the extremal conformal measures to the eigenmeasures of a suitable Ruelle operator. Using Ancona’s theorem, adapted to the Ruelle operator setting, we show that if the group of deck transformations G is hyperbolic then the extremal conformal measures and the hyperbolic boundary of G coincide. We then interpret these results in terms of the asymptotic behavior of cutting sequences of geodesics on a regular cover of a compact hyperbolic surface.
2014 ◽
Vol 36
(2)
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pp. 649-670
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1970 ◽
Vol 13
(1)
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pp. 15-16
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1986 ◽
Vol 149
(8)
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pp. 709
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