A1 Journal article (refereed)
Optimal Extensions of Conformal Mappings from the Unit Disk to Cardioid-Type Domains (2020)

Xu, Haiqing (2020). Optimal Extensions of Conformal Mappings from the Unit Disk to Cardioid-Type Domains. Journal of Geometric Analysis, First Online. DOI: 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: 2020

Volume: First Online

Publisher: Springer

Publication country: United States

Publication language: English

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

Open Access: Open access publication published in a hybrid 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


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

Contributing organizations

Related projects

Centre of Excellence in Analysis and Dynamics Research
Koskela, Pekka
Academy of Finland

Ministry reporting: No, publication in press

Preliminary JUFO rating: 2

Last updated on 2020-18-08 at 13:43