We consider deformations of a group of circle diffeomorphisms with Hölder continuous derivative in the framework of quasiconformal Teichmüller theory and show certain rigidity under conjugation by symmetric homeomorphisms of the circle. As an application, we give a condition for such a diffeomorphism group to be conjugate to a Möbius group by a diffeomorphism of the same regularity. The strategy is to find a fixed point of the group which acts isometrically on the integrable Teichmüller space with the Weil-Petersson metric.2010 Mathematics Subject Classification. Primary 30F60, Secondary 37E30.
In this paper we investigate the Hausdorff dimension of the limit set of an infinitely
generated discrete subgroup of hyperbolic isometries and obtain conditions for the
limit set to have full dimension.
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