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On Ruelle's property

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arxiv 1906.01291 v1 pith:IWHMQLHO submitted 2019-06-04 math.CV

Huo Shengjin , Michel Zinsmeister This is my paper · ORCID
classification math.CV
keywords propertyruellefuchsianfirstresultsgroupgroupskind
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In this paper we investigate the range of validity of Ruelle's property. First, we show that every finitely-generated Fuchsian group has Ruelle's property. We also prove the existence of an infinitely-generated Fuchsian group satisfying Ruelle's property. Concerning the negative results we first generalize Astala-Zinsmeister's results by proving that all convergence Fuchsian groups of the first kind fail to have Ruelle's property. At last, we also give some results about the second kind Fuchsian groups.

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  1. On Carleson measures induced by Beltrami coefficients being compatible with Fuchsian groups

    math.CV 2019-08 reject novelty 5.0 of 10

    For a convex cocompact Fuchsian group of the second kind, a Carleson condition on the free edges of the Dirichlet domain is claimed to imply the induced measure is a Carleson measure on the whole disk.

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