Mutual absolute continuity of interior and exterior harmonic measure implies rectifiability
Classical Analysis and ODEs
2016-06-01 v2 Analysis of PDEs
Metric Geometry
Abstract
We show that, for disjoint domains in the Euclidean space whose boundaries satisfy a non-degeneracy condition, mutual absolute continuity of their harmonic measures implies absolute continuity with respect to surface measure and rectifiability in the intersection of their boundaries.
Keywords
Cite
@article{arxiv.1602.01397,
title = {Mutual absolute continuity of interior and exterior harmonic measure implies rectifiability},
author = {Jonas Azzam and Mihalis Mourgoglou and Xavier Tolsa},
journal= {arXiv preprint arXiv:1602.01397},
year = {2016}
}
Comments
Made suggested changes by referee. To appear in Comm. Pure Appl. Math