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arXiv · 1505.01503

Harmonic measure and approximation of uniformly rectifiable sets

Simon Bortz·Steve Hofmann
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Abstract

Let $E\subset \mathbb{R}^{n+1}$, $n\ge 1$, be a uniformly rectifiable set of dimension $n$. We show $E$ that has big pieces of boundaries of a class of domains which satisfy a 2-sided corkscrew condition, and whose connected components are all chord-arc domains (with uniform control of the various constants). As a consequence, we deduce that $E$ has big pieces of sets for which harmonic measure belongs to weak-$A_\infty$

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Simon Bortz, Steve Hofmann. 2015-05-06. Harmonic measure and approximation of uniformly rectifiable sets. https://arxiv.org/abs/1505.01503

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