On lengths, areas and Lipschitz continuity of polyharmonic mappings

J. Chen; A. Rasila; X. Wang

doi:10.1016/j.jmaa.2014.09.052

On lengths, areas and Lipschitz continuity of polyharmonic mappings

J. Chen, A. Rasila^*, X. Wang

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

In this paper, we continue our investigation of polyharmonic mappings in the complex plane. First, we establish two Landau type theorems. We also show a three circles type theorem and an area version of the Schwarz lemma. Finally, we study Lipschitz continuity of polyharmonic mappings with respect to the distance ratio metric.

Original language	English
Pages (from-to)	1196-1212
Number of pages	17
Journal	Journal of Mathematical Analysis and Applications
Volume	422
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2014.09.052
State	Published - 15 Feb 2015
Externally published	Yes

Keywords

Area distortion
Length distortion
Lipschitz continuity
Polyharmonic mapping

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10.1016/j.jmaa.2014.09.052

Cite this

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title = "On lengths, areas and Lipschitz continuity of polyharmonic mappings",

abstract = "In this paper, we continue our investigation of polyharmonic mappings in the complex plane. First, we establish two Landau type theorems. We also show a three circles type theorem and an area version of the Schwarz lemma. Finally, we study Lipschitz continuity of polyharmonic mappings with respect to the distance ratio metric.",

keywords = "Area distortion, Length distortion, Lipschitz continuity, Polyharmonic mapping",

author = "J. Chen and A. Rasila and X. Wang",

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year = "2015",

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day = "15",

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T1 - On lengths, areas and Lipschitz continuity of polyharmonic mappings

AU - Chen, J.

AU - Rasila, A.

AU - Wang, X.

PY - 2015/2/15

Y1 - 2015/2/15

N2 - In this paper, we continue our investigation of polyharmonic mappings in the complex plane. First, we establish two Landau type theorems. We also show a three circles type theorem and an area version of the Schwarz lemma. Finally, we study Lipschitz continuity of polyharmonic mappings with respect to the distance ratio metric.

AB - In this paper, we continue our investigation of polyharmonic mappings in the complex plane. First, we establish two Landau type theorems. We also show a three circles type theorem and an area version of the Schwarz lemma. Finally, we study Lipschitz continuity of polyharmonic mappings with respect to the distance ratio metric.

KW - Area distortion

KW - Length distortion

KW - Lipschitz continuity

KW - Polyharmonic mapping

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U2 - 10.1016/j.jmaa.2014.09.052

DO - 10.1016/j.jmaa.2014.09.052

M3 - 文章

AN - SCOPUS:84908181367

SN - 0022-247X

VL - 422

SP - 1196

EP - 1212

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

On lengths, areas and Lipschitz continuity of polyharmonic mappings

Abstract

Keywords

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