A note on mappings preserving harmonic measure | Zendy

Stamatis Pouliasis | Zendy; Alexander Yu. Solynin | Zendy

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A note on mappings preserving harmonic measure

Author(s) -

Stamatis Pouliasis,

Alexander Yu. Solynin

Publication year - 2019

Publication title -

proceedings of the american mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.968

H-Index - 84

eISSN - 1088-6826

pISSN - 0002-9939

DOI - 10.1090/proc/14870

Subject(s) - measure (data warehouse) , harmonic measure , mathematics , harmonic , computer science , pure mathematics , harmonic function , data mining , physics , acoustics

In this note we study mappings f f preserving harmonic measures of boundary sets. We show that every homeomorphism f : D ¯ → Ω ¯ f:\overline {D}\to \overline {\Omega } between Greenian domains D D and Ω \Omega in R n \mathbb {R}^n , n ≥ 2 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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