On extendibility of a map induced by the Bers isomorphism

Abstract

Abstract. Let S be a closed Riemann surface of genus g(≧ 2) and setṠ = S \ {ẑ 0 }. Then we have the composed map ϕ • r of a map r : T (S) × U → F (S) and the Bers isomorphism ϕ : F (S) → T (Ṡ), where F (S) is the Bers fiber space of S, T (X) is the Teichmüller space of X and U is the upper half-plane.The purpose of this paper is to show the map ϕ • r : T (S) × U → T (Ṡ). has a continuous extension to some subset of the boundary T (S) × ∂U .