Conformal Contractions and Lower Bounds on the Density of Harmonic Measure

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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 languageEnglish (US)
Pages (from-to)385-391
Number of pages7
JournalPotential Analysis
Volume46
Issue number2
DOIs
StatePublished - Feb 1 2017

Keywords

  • Conformal map
  • Green’s function
  • Harmonic measure

ASJC Scopus subject areas

  • Analysis

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