A note on mappings preserving harmonic measure

Pouliasis, Stamatis; Solynin, Alexander

doi:10.1090/proc/14870

A note on mappings preserving harmonic measure
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by Stamatis Pouliasis and Alexander Yu. Solynin PDF

Proc. Amer. Math. Soc. 148 (2020), 2079-2089 Request permission

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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