Mutual Absolute Continuity of Interior and Exterior Harmonic Measure Implies Rectifiability

Jonas Azzam; Mihalis Mourgoglou; Xavier Tolsa

doi:10.1002/cpa.21687

Mutual Absolute Continuity of Interior and Exterior Harmonic Measure Implies Rectifiability

Jonas Azzam, Mihalis Mourgoglou, Xavier Tolsa

Research output: Contribution to journal › Article › Research › peer-review

17 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 language	English
Pages (from-to)	2121-2163
Journal	Communications on Pure and Applied Mathematics
Volume	70
Issue number	11
DOIs	https://doi.org/10.1002/cpa.21687
Publication status	Published - 1 Nov 2017

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AB - © 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.

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Mutual Absolute Continuity of Interior and Exterior Harmonic Measure Implies Rectifiability

Abstract

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