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∞.
Bibliographical noteFunding Information:
The authors were supported by NSF grant DMS-1361701.
© European Mathematical Society.
- Carleson measures
- Harmonic measure
- Uniform rectifiability