A note on mappings preserving harmonic measure

Stamatis Pouliasis; Alexander Solynin

A note on mappings preserving harmonic measure

Mathematics and Statistics

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Abstract

Abstract. In this note we study mappings f preserving harmonic measures of boundary sets. We show that every homeomorphism f : D ! between Greenian domains D and in Rn, n 2, preserving harmonic measures, is a harmonic morphism. We also study problems on conformality of mappings preserving harmonic measures of some specic sets on the boundaries of planar domains.

Original language	English
Pages (from-to)	2079-2089
Journal	Proceedings of the American Mathematical Society.
State	Published - May 1 2020

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title = "A note on mappings preserving harmonic measure",

abstract = "Abstract. In this note we study mappings f preserving harmonic measuresof boundary sets. We show that every homeomorphism f : D ! between Greenian domains D and in Rn, n 2, preserving harmonicmeasures, is a harmonic morphism. We also study problems on conformalityof mappings preserving harmonic measures of some specic setson the boundaries of planar domains.",

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AU - Solynin, Alexander

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N2 - Abstract. In this note we study mappings f preserving harmonic measuresof boundary sets. We show that every homeomorphism f : D ! between Greenian domains D and in Rn, n 2, preserving harmonicmeasures, is a harmonic morphism. We also study problems on conformalityof mappings preserving harmonic measures of some specic setson the boundaries of planar domains.

AB - Abstract. In this note we study mappings f preserving harmonic measuresof boundary sets. We show that every homeomorphism f : D ! between Greenian domains D and in Rn, n 2, preserving harmonicmeasures, is a harmonic morphism. We also study problems on conformalityof mappings preserving harmonic measures of some specic setson the boundaries of planar domains.

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EP - 2089

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

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