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A note on mappings preserving harmonic measure


Authors: Stamatis Pouliasis and Alexander Yu. Solynin
Journal: Proc. Amer. Math. Soc. 148 (2020), 2079-2089
MSC (2010): Primary 30C20, 30C75
DOI: https://doi.org/10.1090/proc/14870
Published electronically: January 13, 2020
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Abstract: In this note we study mappings $ f$ preserving harmonic measures of boundary sets. We show that every homeomorphism $ f:\overline {D}\to \overline {\Omega }$ between Greenian domains $ D$ and $ \Omega $ in $ \mathbb{R}^n$, $ n\ge 2$, preserving harmonic measures, is a harmonic morphism. We also study problems on conformality of mappings preserving harmonic measures of some specific sets on the boundaries of planar domains.


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Stamatis Pouliasis
Affiliation: Texas Tech University-Costa Rica, Avenida Escazú, Edificio AE205, San Jose, 10203 Costa Rica
Address at time of publication: Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas 79409
Email: stamatis.pouliasis@ttu.edu

Alexander Yu. Solynin
Affiliation: Texas Tech University-Costa Rica, Avenida Escazú, Edificio AE205, San Jose, 10203 Costa Rica
Address at time of publication: Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas 79409
Email: alex.solynin@ttu.edu

DOI: https://doi.org/10.1090/proc/14870
Keywords: Harmonic measure, harmonic morphism, conformal mapping
Received by editor(s): May 29, 2019
Received by editor(s) in revised form: September 13, 2019
Published electronically: January 13, 2020
Communicated by: Jeremy Tyson
Article copyright: © Copyright 2020 American Mathematical Society