Mutual absolute continuity of interior and exterior harmonic measure implies rectifiability

Jonas Azzam, Mihalis Mourgoglou, Xavier Tolsa

Research output: Contribution to journalArticlepeer-review

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.
Original languageEnglish
Pages (from-to)2121-2163
Number of pages37
JournalCommunications on Pure and Applied Mathematics
Volume70
Issue number11
Early online date15 Feb 2017
DOIs
Publication statusPublished - Nov 2017
Externally publishedYes

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