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SPHERICALIZATION AND FLATTENING PRESERVE UNIFORM DOMAINS IN NONLOCALLY COMPACT METRIC SPACES

Part of: Geometric function theory Riemann surfaces

Published online by Cambridge University Press:  27 February 2020

YAXIANG LI ,
SAMINATHAN PONNUSAMY Open the ORCID record for SAMINATHAN PONNUSAMY [Opens in a new window]  and
QINGSHAN ZHOU
YAXIANG LI
Affiliation:
Department of Mathematics, Hunan First Normal University, Changsha, Hunan 410205, PR China e-mail: yaxiangli@163.com
SAMINATHAN PONNUSAMY
Affiliation:
Department of Mathematics, Indian Institute of Technology Madras, Chennai-600 036, India e-mail: samy@iitm.ac.in
QINGSHAN ZHOU
Affiliation:
School of Mathematics and Big Data, Foshan University, Foshan, Guangdong 528000, PR China e-mail: q476308142@qq.com
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Abstract

The main aim of this paper is to investigate the invariant properties of uniform domains under flattening and sphericalization in nonlocally compact complete metric spaces. Moreover, we show that quasi-Möbius maps preserve uniform domains in nonlocally compact spaces as well.

Keywords

uniform domainsflatteningsphericalizationquasi-Möbiusquasisymmetricquasihyperbolic metric

MSC classification

Primary: 30C65: Quasiconformal mappings in $^n$, other generalizations 30F45: Conformal metrics (hyperbolic, Poincaré, distance functions)
Secondary: 30C20: Conformal mappings of special domains

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 112 , Issue 1 , February 2022 , pp. 68 - 89
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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Footnotes

Communicated by W. Moors

The first author was supported by NNSF of China (nos 11601529, 11671127, 11971124). The third author was supported by NNSF of China (nos 11901090, 11571216), and by Department of Education of Guangdong Province, China (grant nos 2018KQNCX285 and 2018KTSCX245).

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