Closed geodesics and non-convexity in asymptotic Teichmüller spaces

摘要

In this paper, the geometric property of asymptotic Teichmüller space is studied. Closed geodesics in any infinite dimensional asymptotic Teichmüller space are constructed, and the non-convexity of spheres in asymptotic Teichmüller space with respect to infinitely many geodesics is proved.