The harmonic and quasiconformal extension operators

Dariusz Partyka; Ken Sakan; Józef Zając

Displaying similar documents to “The harmonic and quasiconformal extension operators”

A distortion theorem for quasiconformal automorphisms of the unit disk

Dariusz Partyka (1991)

Annales Polonici Mathematici

Similarity:

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

A remark on polygonal quasiconformal maps.

Krushkal, S.L. (2001)

Georgian Mathematical Journal

Similarity:

A bound for reflections across Jordan curves.

Krushkal, Samuel L. (2003)

Georgian Mathematical Journal

Similarity:

The Douady-Earle extension of quasihomographies

Ken-Ichi Sakan, Józef Zając (1996)

Banach Center Publications

Similarity:

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 $E_{f}$ .

Dirichlet's Principle, Uniqueness of Harmonic Maps and Extremal QC Mappings

Miodrag Mateljević (2004)

Zbornik Radova

Similarity:

Quasiconformal Harmonic Functions Between Convex Domains

David Kalaj (2004)

Publications de l'Institut Mathématique

Similarity:

Removable singularities for Hölder continuous quasiregular mappings in the plane.

Clop, Albert (2007)

Annales Academiae Scientiarum Fennicae. Mathematica

Similarity:

Modulus of continuity for quasiregular mappings with finite distortion extension.

Zapadinskaya, Aleksandra (2008)

Annales Academiae Scientiarum Fennicae. Mathematica

Similarity:

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

Dariusz Partyka (1995)

Banach Center Publications

Similarity:

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 $A_{γ} : ℍ \to ℍ$ is determined by the maximal dilatation of φ. A characterization of all eigenvalues of a quasisymmetric automorphism γ in terms of the smallest...

On boundary homeomorphisms of trans-quasiconformal maps of the disk.

Zakeri, Saeed (2008)

Annales Academiae Scientiarum Fennicae. Mathematica

Similarity:

Nonlinear analysis and quasiconformal mappings from the perspective of PDEs

Tadeusz Iwaniec (1999)

Banach Center Publications

Similarity:

Contents Introduction 119 1. Quasiregular mappings 120 2. The Beltrami equation 121 3. The Beltrami-Dirac equation 122 4. A quest for compactness 124 5. Sharp $L^{p}$ -estimates versus variational integrals 125 6. Very weak solutions 128 7. Nonlinear commutators 129 8. Jacobians and wedge products 131 9. Degree formulas 134 References 136