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Quasihomographies in the theory of Teichmüller spaces

Zając Józef — 1996

CONTENTSIntroduction............................................................................................................................5 I. Special functions of quasiconformal theory.....................................................................10 1. Introduction.................................................................................................................10 2. The distortion function $Φ_{K}$ .....................................................................................11 3....

The rosettes.

Waldemar Cieslak; Józef Zajac — 1986

Mathematica Scandinavica

The Douady-Earle extension of quasihomographies

Ken-Ichi Sakan; Józef Zając — 1996

Banach Center Publications

Quasihomography is a useful notion to represent a sense-preserving automorphism of the unit circle T which admits a quasiconformal extension to the unit disc. For K ≥ 1 let $A_{T} (K)$ denote the family of all K-quasihomographies of T. With any $f \in A_{T} (K)$ we associate the Douady-Earle extension $E_{f}$ and give an explicit and asymptotically sharp estimate of the $L_{\infty}$ norm of the complex dilatation of $E_{f}$ .

The harmonic and quasiconformal extension operators

Dariusz Partyka; Ken Sakan; Józef Zając — 1999

Banach Center Publications

Different aspects of the boundary value problem for quasiconformal mappings and Teichmüller spaces are expressed in a unified form by the use of the trace and extension operators. Moreover, some new results on harmonic and quasiconformal extensions are included.

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Quasihomographies in the theory of Teichmüller spaces

The rosettes.

The Douady-Earle extension of quasihomographies

The harmonic and quasiconformal extension operators