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 › peer-review

Abstract / Description of output

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 language	English
Pages (from-to)	2121-2163
Number of pages	37
Journal	Communications on Pure and Applied Mathematics
Volume	70
Issue number	11
Early online date	15 Feb 2017
DOIs	https://doi.org/10.1002/cpa.21687
Publication status	Published - Nov 2017
Externally published	Yes

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https://arxiv.org/abs/1602.01397Licence: Creative Commons: Attribution (CC-BY)

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title = "Mutual absolute continuity of interior and exterior harmonic measure implies rectifiability",

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. ",

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AU - Mourgoglou, Mihalis

AU - Tolsa, Xavier

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N2 - 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.

AB - 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.

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DO - 10.1002/cpa.21687

M3 - Article

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EP - 2163

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

IS - 11

ER -

Mutual absolute continuity of interior and exterior harmonic measure implies rectifiability

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