The Universal Teichmüller Space and Function Space. (21st January 2020) - Liu, Yutong; Qi, Yi
Abstract : In this paper, a subspace T F 0 2, 1 − s, s of the universal Teichmüller space, which is related to the analytic function space F 0 2, 1 − s, s, is introduced and the holomorphy of the Bers map is shown. It is also proved that the pre-Bers map is holomorphic and the prelogarithmic derivative model T ˜ F 0 2, 1 − s, s of T F 0 2, 1 − s, s is a disconnected subset of the function space F 0 2, 1 − s, s . Moreover, several equivalent descriptions of elements of T F 0 2, 1 − s, s are obtained and the holomorphy of higher Bers maps is proved.