Conformal Contractions and Lower Bounds on the Density of Harmonic Measure

Research output: Research - peer-reviewArticle

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.

LanguageEnglish (US)
Pages1-7
Number of pages7
JournalPotential Analysis
DOIs
StateAccepted/In press - Aug 31 2016

Fingerprint

Harmonic Measure
Contraction
Lower bound
Nonexpansive Map
Conformal Map
Unit Disk
High-dimensional
Analogue
Sufficient Conditions
Class

Keywords

  • Conformal map
  • Green’s function
  • Harmonic measure

ASJC Scopus subject areas

  • Analysis

Cite this

Conformal Contractions and Lower Bounds on the Density of Harmonic Measure. / Kovalev, Leonid V.

In: Potential Analysis, 31.08.2016, p. 1-7.

Research output: Research - peer-reviewArticle

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