Barycentric extension and the Bers embedding for asymptotic Teichmüller space

Abstract

In this paper we show that the Bers map of the asymptotic Teichmüller space AT(X) of an arbitrary hyperbolic Riemann surface X is injective. We prove further that AT(X) and the fibers of the quotient may from T(X) to AT(X) are contractible and that every point in the fiber over the basepoint of AT(X) is represented by a quasiconformal map that is an asymptotic hyperbolic isometry. The barycentric extension operators plays a central role in our proofs.

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