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QUASICONFORMAL HARMONIC MAPPINGS BETWEEN DOMAINS CONTAINING INFINITY

Part of: Two-dimensional theory Geometric function theory

Published online by Cambridge University Press:  08 January 2020

DAVID KALAJ
DAVID KALAJ*
Affiliation:
Faculty of Natural Sciences and Mathematics,University of Montenegro, Cetinjski put b.b. 81000Podgorica, Montenegro email davidk@ac.me
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Abstract

Assume that $\unicode[STIX]{x1D6FA}$ and $D$ are two domains with compact smooth boundaries in the extended complex plane $\overline{\mathbf{C}}$. We prove that every quasiconformal mapping between $\unicode[STIX]{x1D6FA}$ and $D$ mapping $\infty$ onto itself is bi-Lipschitz continuous with respect to both the Euclidean and Riemannian metrics.

Keywords

quasiconformal mappingscomplement of the unit diskquasi-isometry

MSC classification

Primary: 31A05: Harmonic, subharmonic, superharmonic functions
Secondary: 30C62: Quasiconformal mappings in the plane
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 102 , Issue 1 , August 2020 , pp. 109 - 117
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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