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A distortion theorem for quasiconformal automorphisms of the unit disk

100%

Partyka D.

Annales Polonici Mathematici

1991

tom 55

nr 1

277-281

We give a distortion theorem for quasiconformal automorphisms of the unit disk and its application to improving some results due to Douady and Earle.

The smallest positive eigenvalue of a quasisymmetric automorphism of the unit circle

88%

Partyka D.

Banach Center Publications

1995

tom 31

nr 1

303-310

This paper provides sufficient conditions on a quasisymmetric automorphism γ of the unit circle which guarantee the existence of the smallest positive eigenvalue of γ. They are expressed by means of a regular quasiconformal Teichmüller self-mapping φ of the unit disc Δ. In particular, the norm of the generalized harmonic conjugation operator $A_γ:ℍ → ℍ$ is determined by the maximal dilatation of φ. A characterization of all eigenvalues of a quasisymmetric automorphism γ in terms of the smallest positive eigenvalue of some other quasisymmetric automorphism σ is given.

The harmonic and quasiconformal extension operators

51%

Partyka D., Sakan K.-I., Zając J.

Banach Center Publications

1999

tom 48

nr 1

141-177

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.

Ograniczanie wyników

2 Banach Center Publications

1 Annales Polonici Mathematici

3 Partyka D.

1 Sakan K.-I.

1 Zając J.

1 1999

1 1995

1 1991

Wyniki wyszukiwania

A distortion theorem for quasiconformal automorphisms of the unit disk

The smallest positive eigenvalue of a quasisymmetric automorphism of the unit circle

The harmonic and quasiconformal extension operators