Harmonic measure and approximation of uniformly rectifiable sets

Simon Bortz; Steve Hofmann

doi:10.4171/rmi/940

Harmonic measure and approximation of uniformly rectifiable sets

Simon Bortz, Steve Hofmann

School of Mathematics

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

Let E ⊂ ℝⁿ⁺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∞.

Original language	English (US)
Pages (from-to)	351-373
Number of pages	23
Journal	Revista Matematica Iberoamericana
Volume	33
Issue number	1
DOIs	https://doi.org/10.4171/rmi/940
State	Published - 2017

Bibliographical note

Funding Information:
The authors were supported by NSF grant DMS-1361701.

Publisher Copyright:
© European Mathematical Society.

Keywords

Carleson measures
Chord-arc
Harmonic measure
NTA
Uniform rectifiability

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10.4171/rmi/940

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abstract = "Let E ⊂ ℝn+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∞.",

keywords = "Carleson measures, Chord-arc, Harmonic measure, NTA, Uniform rectifiability",

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AU - Bortz, Simon

AU - Hofmann, Steve

N1 - Funding Information: The authors were supported by NSF grant DMS-1361701. Publisher Copyright: © European Mathematical Society.

PY - 2017

Y1 - 2017

N2 - Let E ⊂ ℝn+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∞.

AB - Let E ⊂ ℝn+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∞.

KW - Carleson measures

KW - Chord-arc

KW - Harmonic measure

KW - NTA

KW - Uniform rectifiability

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Harmonic measure and approximation of uniformly rectifiable sets

Abstract

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