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.
- Publication:
-
arXiv e-prints
- Pub Date:
- January 2016
- DOI:
- 10.48550/arXiv.1601.02711
- arXiv:
- arXiv:1601.02711
- Bibcode:
- 2016arXiv160102711K
- Keywords:
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- Mathematics - Complex Variables;
- 30C62;
- 31A15;
- 31B05
- E-Print:
- 7 pages, 1 figure