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arXiv · 1601.02711

Conformal contractions and lower bounds on the density of harmonic measure

Leonid V. Kovalev
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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.

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Leonid V. Kovalev. 2016-06-29. Conformal contractions and lower bounds on the density of harmonic measure. https://doi.org/10.1007/s11118-016-9586-6

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