Conformal contractions and lower bounds on the density of harmonic measure

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.

arXiv comment7 pages, 1 figure

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