A Sufficient Condition for Rigidity in Extremality of Teichmüller Equivalence Classes by Schwarzian Derivative

Abstract

The Strebel point is a Teichmüller equivalence class in the Teichmüller space that has a certain rigidity in the extremality of the maximal dilatation. In this paper, we give a sufficient condition in terms of the Schwarzian derivative for a Teichmüller equivalence class of the universal Teichmüller space under which the class is a Strebel point. As an application, we construct a Teichmüller equivalence class that is a Strebel point and that is not an asymptotically conformal class.