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arXiv · 1602.01397

Mutual absolute continuity of interior and exterior harmonic measure implies rectifiability

Jonas Azzam·Mihalis Mourgoglou·Xavier Tolsa
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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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Jonas Azzam, Mihalis Mourgoglou, Xavier Tolsa. 2016-02-03. Mutual absolute continuity of interior and exterior harmonic measure implies rectifiability. https://arxiv.org/abs/1602.01397

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