The problem of holomorphic contractibilty of Teichm\"uller spaces T(0, n) of the punctures spheres (n > 4) arose in the 1970s in connection with solving the algebraic equations in Banach algebras. We provide a positive solution of this problem.

We show by simple explicit constructions that the Teichmuller spaces To(Δ) and To(Δ \ {0}) are holomorphically contractible. We also call attention to a useful criterion for a map between domains in… Expand

A Portmanteau of Preliminaries The Moduli Spaces For Riemann Surfaces The Complex Structure of Teichmuller Spaces More About the Complex Structure of Teichmuller Spaces The Universal Family and Its… Expand

We provide a negative answer to Royden’s problem whether any finite dimensional Teichmüller space of dimension greater than 1 is biholomorhically equivalent to a bounded convex domain in complex… Expand

Under review is a book on quasiconformal mappings and their role in the study of Riemann surfaces and Kleinian groups. Since quasiconformal mappings are beginning to find applications outside of… Expand

In this paper we consider the problem of the starlikeness of Teichmüller spaces for finite-dimensional spaces. It is shown that in high dimensions the answer is negative. 1. Introductory remarks In… Expand

I Quasiconformal Mappings.- to Chapter I.- 1. Conformal Invariants.- 1.1 Hyperbolic metric.- 1.2 Module of a quadrilateral.- 1.3 Length-area method.- 1.4 Rengel's inequality.- 1.5 Module of a ring… Expand