Conformal Contractions and Lower Bounds on the Density of Harmonic Measure

Leonid V. Kovalev

doi:10.1007/s11118-016-9586-6

Conformal Contractions and Lower Bounds on the Density of Harmonic Measure

Leonid V. Kovalev

Department of Mathematics

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

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)	385-391
Number of pages	7
Journal	Potential Analysis
Volume	46
Issue number	2
DOIs	https://doi.org/10.1007/s11118-016-9586-6
State	Published - Feb 1 2017

Keywords

Conformal map
Green’s function
Harmonic measure

ASJC Scopus subject areas

Analysis

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N2 - 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.

AB - 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.

KW - Conformal map

KW - Green’s function

KW - Harmonic measure

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Conformal Contractions and Lower Bounds on the Density of Harmonic Measure

Abstract

Keywords

ASJC Scopus subject areas

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