Conformal Contractions and Lower Bounds on the Density of Harmonic Measure

Leonid V. Kovalev

Research output: Contribution to journal › Article

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
Nonexpansive Map
Lower bound
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: Contribution to journal › Article

Kovalev, LV 2016, 'Conformal Contractions and Lower Bounds on the Density of Harmonic Measure' Potential Analysis, pp. 1-7. DOI: 10.1007/s11118-016-9586-6
Kovalev LV. Conformal Contractions and Lower Bounds on the Density of Harmonic Measure. Potential Analysis. 2016 Aug 31;1-7. Available from, DOI: 10.1007/s11118-016-9586-6
Kovalev, Leonid V./ Conformal Contractions and Lower Bounds on the Density of Harmonic Measure. In: Potential Analysis. 2016 ; pp. 1-7
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