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2009年07月23日

【期刊论文】ON THE EXTREMALITY OF QUASICONFORMAL MAPPINGS AND QUASICONFORMAL DEFORMATIONS

沈玉良， SHEN YU-LIANG

Article electronically published on June 30, 1999 135-139，-0001，（）：

-1年11月30日

rmine,for each fixde t＞0,whether the extremality of f(z,t)is equivalent to that of F(w,t).The note gives this a negative qpproach in both directions.

Quasiconformal mapping,， quasiconformal deformation,， extremality.，

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2009年07月23日

【期刊论文】A NOTE ON HAMILTON SEQUENCES FOR EXTREMAL BELTRAMI COEFFICIENTS

沈玉良， SHEN YU-LIANG

Article electronically published on July 27, 2000 105-109，-0001，（）：

-1年11月30日

摘要

ABSTRACT. F. P. Gardiner gave a sufficient condition for a sequence to be a Hamilton sequence for an extremal Beltrami coefficient.Inthis note, we shallconsider the converse problem, proving that the condition is not necessary.

Hamilton sequence,， extremal Beltrami coecient,， Teichmuller metric.，

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2009年07月23日

【期刊论文】ON THE UNIQUE EXTREMALITY OF QUASICONFORMAL MAPPINGS WITH DILATATION BOUNDS

沈玉良， Yu-LIANG SHEN

Tohoku Math. J. 56 (2004), 105-123，-0001，（）：

-1年11月30日

摘要

Concerning the problem of extremality of quasiconf'ormal mappings withdilatation bounds. we discuss the unique extremality of the problem and prove the if part of aconjecture on the unique extremality ([GI], [RI]). To this end. we need to investigate a newextremal problem in the infinitesimal setting. In particular, we give a complete description ofthe unique infinitesimal extremality of partially zero Beltrami differentials.

Quasiconformal mapping,， Beltrami differential,， uniquely extremal,， uniquely infinitesimally extremal.，

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2009年07月23日

【期刊论文】CONFORMAL INVARIANTS OF QED DOMAINS

沈玉良， Yu-LIANG SHEN

Tohoku Math. J. 56 (2004), 445-466，-0001，（）：

-1年11月30日

摘要

Given a Jordan domain Ω in the extended complex plane C, denote byMb(Ω), M(Ω) and R(Ω) the boundary quasiextremal distance constant, quasiextremal dis-tance constant and quasiconformal reflection constantofS2.respectively. It is known thatMb(Ω)<M(Ω)<R(Ω)+1. In this paper, we will give some further relations amongMb (Ω), M(Ω) and R (Ω) by introducing and studying some other closely related constants.Particularly, we will give a necessary and sufficient condition for Mb(Ω) = R(Ω)+1 andshow that M(Ω)<R (Ω)+I for all asymptoticajly conformal extension domains other thandisks. This gives an affirmative answer to a question asked by Yang, showing that the con jecture M(Ω)=R(Ω)+I by Garnett and Yang is not true for all asymptoticallyconformalextension domains other than disks. Our discussion relies heavily on the theory of extremalquasiconformal mappings. which in turn gives some interesting results in the extremal quasi-conformal mapping theory as well.

Boundary quasiextremal distance constant,， quasiextremal distance constant,， quasiconformal reflection constant,， quasisymmetric homeomorphism,， QED domain.，

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2009年07月23日

【期刊论文】VARIOUS CONSTANTS ASSOCIATED WITH QUASIDISKS AND QU ASISYMMETRIC HOMEOMORPHISMS

沈玉良， Shen Yu-Liang

Nouvelle serie, tome 75 (89) (2004), 95-107，-0001，（）：

-1年11月30日

摘要

In this expository paper, we willdiscusssomeconstants asso-ciated with quasidisks andquasisvmmetrichomeomorphisms.

quasidisk,， quasisymmetric homeomorphism,， quasiconformal mapping,， harmonic function,， Fredholm eigenvalue,， Schober functional,， boundary quasiextremal distance constant,， quasiextremal distance constant,， quasiconformal reflection constant,， extremal maximal dilatation,， boundary dilatation,， maximal dilatation.， .，

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