Optimal Extensions of Conformal Mappings from the Unit Disk to Cardioid-Type Domains
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
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Journal of Geometric AnalysisDate
2021Copyright
© 2020 the Author(s)
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.
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1050-6926Publication in research information system
https://converis.jyu.fi/converis/portal/detail/Publication/34159634
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Centre of Excellence, AoFAdditional information about funding
Open access funding provided by University of Jyväskylä (JYU). The author has been supported by China Scholarship Council (project No.201706340060) and Academy of Finland via the Centre of Excellence in Analysis and Dynamics Research (Grant No. 307333).License
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