Mutual Absolute Continuity of Interior and Exterior Harmonic Measure Implies Rectifiability

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 Per...

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Bibliographic Details
Published in:Communications on pure and applied mathematics 2017-11, Vol.70 (11), p.2121-2163
Main Authors: Azzam, Jonas, Mourgoglou, Mihalis, Tolsa, Xavier
Format: Article
Language:English
Subjects:
Boundaries
Continuity
Euclidean geometry
Euclidean space
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Summary: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.
ISSN:0010-3640
1097-0312
DOI:10.1002/cpa.21687