Mutual Absolute Continuity of Interior and Exterior Harmonic Measure Implies Rectifiability

Jonas Azzam, Mihalis Mourgoglou, Xavier Tolsa

Research output: Contribution to journalArticleResearchpeer-review

16 Citations (Scopus)

Abstract

© 2017 Wiley Periodicals, Inc. 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.
Original languageEnglish
Pages (from-to)2121-2163
JournalCommunications on Pure and Applied Mathematics
Volume70
Issue number11
DOIs
Publication statusPublished - 1 Nov 2017

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