A1 Journal article (refereed)
Optimal Extensions of Conformal Mappings from the Unit Disk to Cardioid-Type Domains (2021)

Xu, H. (2021). Optimal Extensions of Conformal Mappings from the Unit Disk to Cardioid-Type Domains. Journal of Geometric Analysis, 31(3), 2296-2330. https://doi.org/10.1007/s12220-019-00340-x

JYU authors or editors

Publication details

All authors or editors: Xu, Haiqing

Journal or series: Journal of Geometric Analysis

ISSN: 1050-6926

eISSN: 1559-002X

Publication year: 2021

Volume: 31

Issue number: 3

Pages range: 2296-2330

Publisher: Springer

Publication country: United States

Publication language: English

DOI: https://doi.org/10.1007/s12220-019-00340-x

Publication open access: Openly available

Publication channel open access: Partially open access channel

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/67370

Web address of parallel published publication (pre-print): https://arxiv.org/abs/1905.09351

Abstract

The conformal mapping f(z)=(z+1)2 from D onto the standard cardioid has a homeomorphic extension of finite distortion to entire R2. We study the optimal regularity of such extensions, in terms of the integrability degree of the distortion and of the derivatives, and these for the inverse. We generalize all outcomes to the case of conformal mappings from D onto cardioid-type domains.

Keywords: analytical geometry

Free keywords: extensions; homeomorphisms of finite distortion; inner cusp

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Ministry reporting: Yes

Reporting Year: 2021

JUFO rating: 2