Harmonic measure and approximation of uniformly rectifiable sets

Simon Bortz, Steve Hofmann

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


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 languageEnglish (US)
Pages (from-to)351-373
Number of pages23
JournalRevista Matematica Iberoamericana
Issue number1
StatePublished - 2017

Bibliographical note

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

Publisher Copyright:
© European Mathematical Society.


  • Carleson measures
  • Chord-arc
  • Harmonic measure
  • NTA
  • Uniform rectifiability


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