On the isometries from the unit disk to infinite dimensional Teichmüller spaces

Abstract

We generalize Earle-Li's polydisk theorem and embedding theorem, and study isometries from the unit disk to infinite dimensional Teichmüller spaces. We also give a simple proof that for any non-Strebel point τ, there exist infinitely many real analytic geodesic disks through τ and the basepoint in infinitely dimensional Teichmüller spaces.