Image of asymptotic Bers map

Abstract

In this paper, we give a geometric characterization for developing mappings such that the asymptotic class of its Schwarzian derivative is in the image of the asymptotic Bers map from the asymptotic Teichmüller space of the unit disk D. We also give a characterization of points in the closure of the image, and discuss the density problem for the asymptotic Teichmüller space.