Invertible harmonic mappings beyond the Kneser theorem and quasiconformal harmonic mappings

David Kalaj

Studia Mathematica (2011)

  • Volume: 207, Issue: 2, page 117-136
  • ISSN: 0039-3223

Abstract

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We extend the Rado-Choquet-Kneser theorem to mappings with Lipschitz boundary data and essentially positive Jacobian at the boundary without restriction on the convexity of image domain. The proof is based on a recent extension of the Rado-Choquet-Kneser theorem by Alessandrini and Nesi and it uses an approximation scheme. Some applications to families of quasiconformal harmonic mappings between Jordan domains are given.

How to cite

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David Kalaj. "Invertible harmonic mappings beyond the Kneser theorem and quasiconformal harmonic mappings." Studia Mathematica 207.2 (2011): 117-136. <http://eudml.org/doc/285376>.

@article{DavidKalaj2011,
abstract = {We extend the Rado-Choquet-Kneser theorem to mappings with Lipschitz boundary data and essentially positive Jacobian at the boundary without restriction on the convexity of image domain. The proof is based on a recent extension of the Rado-Choquet-Kneser theorem by Alessandrini and Nesi and it uses an approximation scheme. Some applications to families of quasiconformal harmonic mappings between Jordan domains are given.},
author = {David Kalaj},
journal = {Studia Mathematica},
keywords = {planar harmonic mappings; quasiconformal mapping; Jordan domains; Rado-Kneser-Choquet theorem},
language = {eng},
number = {2},
pages = {117-136},
title = {Invertible harmonic mappings beyond the Kneser theorem and quasiconformal harmonic mappings},
url = {http://eudml.org/doc/285376},
volume = {207},
year = {2011},
}

TY - JOUR
AU - David Kalaj
TI - Invertible harmonic mappings beyond the Kneser theorem and quasiconformal harmonic mappings
JO - Studia Mathematica
PY - 2011
VL - 207
IS - 2
SP - 117
EP - 136
AB - We extend the Rado-Choquet-Kneser theorem to mappings with Lipschitz boundary data and essentially positive Jacobian at the boundary without restriction on the convexity of image domain. The proof is based on a recent extension of the Rado-Choquet-Kneser theorem by Alessandrini and Nesi and it uses an approximation scheme. Some applications to families of quasiconformal harmonic mappings between Jordan domains are given.
LA - eng
KW - planar harmonic mappings; quasiconformal mapping; Jordan domains; Rado-Kneser-Choquet theorem
UR - http://eudml.org/doc/285376
ER -

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