Conformal Contractions and Lower Bounds on the Density of Harmonic Measure

Leonid Vladimirovich Kovalev

doi:10.1007/s11118-016-9586-6

Conformal Contractions and Lower Bounds on the Density of Harmonic Measure

Leonid Vladimirovich Kovalev

Department of Mathematics

Research output: Contribution to journal › Article

1 Scopus citations

Abstract

We give a concrete sufficient condition for a simply-connected domain to be the image of the unit disk under a nonexpansive conformal map. This class of domains is also characterized by having sufficiently dense harmonic measure. The relation with the harmonic measure provides a natural higher-dimensional analogue of this problem, which is also addressed.

Original language	English (US)
Pages (from-to)	1-7
Number of pages	7
Journal	Potential Analysis
DOIs	https://doi.org/10.1007/s11118-016-9586-6
State	Accepted/In press - Aug 31 2016

Keywords

Conformal map
Green’s function
Harmonic measure

ASJC Scopus subject areas

Analysis

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Kovalev, L. V. (Accepted/In press). Conformal Contractions and Lower Bounds on the Density of Harmonic Measure. Potential Analysis, 1-7. https://doi.org/10.1007/s11118-016-9586-6

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