Mutual Absolute Continuity of Interior and Exterior Harmonic Measure Implies Rectifiability
Jonas Azzam, Mihalis Mourgoglou, Xavier Tolsa · Communications on Pure and Applied Mathematics · 2017
Abstract We show that, for disjoint domains in the euclidean space whose boundaries satisfy a nondegeneracy condition, mutual absolute continuity of their harmonic measures implies absolute continuity with respect to surface measure and rectifiability in the intersection of their boundaries. © 2017 Wiley Periodicals, Inc.