A note on mappings preserving harmonic measure

Stamatis Pouliasis; Alexander Y.U. Solynin

doi:10.1090/proc/14870

A note on mappings preserving harmonic measure

Stamatis Pouliasis, Alexander Y.U. Solynin

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

In this note we study mappings f preserving harmonic measures of boundary sets. We show that every homeomorphism f : D → Ω between Greenian domains D and Ω in Rⁿ, n ≥ 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.

Original language	English
Pages (from-to)	2079-2089
Number of pages	11
Journal	Proceedings of the American Mathematical Society
Volume	148
Issue number	5
DOIs	https://doi.org/10.1090/proc/14870
State	Published - 2020

Keywords

Conformal mapping
Harmonic measure
Harmonic morphism

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abstract = "In this note we study mappings f preserving harmonic measures of boundary sets. We show that every homeomorphism f : D → Ω between Greenian domains D and Ω in Rn, n ≥ 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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AU - Pouliasis, Stamatis

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AB - In this note we study mappings f preserving harmonic measures of boundary sets. We show that every homeomorphism f : D → Ω between Greenian domains D and Ω in Rn, n ≥ 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.

KW - Conformal mapping

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KW - Harmonic morphism

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JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

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A note on mappings preserving harmonic measure

Abstract

Keywords

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