Revista Matemática Iberoamericana


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Volume 33, Issue 1, 2017, pp. 351–373
DOI: 10.4171/RMI/940

Published online: 2017-02-22

Harmonic measure and approximation of uniformly rectifiable sets

Simon Bortz[1] and Steve Hofmann[2]

(1) Mathematical Sciences Research Institute, Berkeley, USA
(2) University of Missouri, Columbia, USA

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-$A_\infty$.

Keywords: Carleson measures, harmonic measure, uniform rectifiability, NTA, chord-arc

Bortz Simon, Hofmann Steve: Harmonic measure and approximation of uniformly rectifiable sets. Rev. Mat. Iberoam. 33 (2017), 351-373. doi: 10.4171/RMI/940