Publications de l’Institut Mathématique, Nouvelle Série, Vol. 102[116], pp. 85

Publications de l’Institut Mathématique, Nouvelle Série
Vol. 102[116], pp. 85–91 (2017)

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Bi-Lipschitzity of quasiconformal harmonic mappings in $n$ -dimensional space with respect to $k$ -metric

Shadia Shalandi

Department of Mathematics, University of Belgrade, Belgrade, Serbia

Abstract: We explore conditions which guarantee bi-Lipschitzity of harmonic quasiconformal maps with respect to $k$ -metric. We prove that harmonic $k$ -quasiconformal maps with nonzero Jacobian between any two domains in $ℝ^{n}$ are bi-Lipschitz with respect to $k$ -metric, and prove the converse too.

Keywords: harmonic maps, quasi-conformal maps, k-metric, bi-Lipschitz maps

Classification (MSC2000): 30C65; 42B37

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Electronic fulltext finalized on: 3 Nov 2017. This page was last modified: 29 Jan 2018.

© 2017 Mathematical Institute of the Serbian Academy of Science and Arts
© 2017–2018 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition

Bi-Lipschitzity of quasiconformal harmonic mappings in n-dimensional space with respect to k-metric

Shadia Shalandi

Bi-Lipschitzity of quasiconformal harmonic mappings in $n$ -dimensional space with respect to $k$ -metric