Rigidity of groups of circle diffeomorphisms and Teichmüller spaces

Abstract

We consider deformations of a group of circle diffeomorphisms with Hölder continuous derivatives 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.

References in corpus (2)

• Teichmüller space of circle diffeomorphisms with Hölder continuous derivatives
• Injectivity of the quotient Bers embedding of Teichmüller spaces

Cited by in corpus (2)

• Teichmüller space of circle diffeomorphisms with Hölder continuous derivatives
• Teichmüller spaces of piecewise symmetric homeomorphisms on the unit circle