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arXiv · 1505.06088

Rectifiability of harmonic measure in domains with porous boundaries

Jonas Azzam·Mihalis Mourgoglou·Xavier Tolsa
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Abstract

We show that if $n\geq 1$, $Ω\subset \mathbb R^{n+1}$ is a connected domain with porous boundary, and $E\subset \partialΩ$ is a set of finite and positive Hausdorff $H^{n}$-measure upon which the harmonic measure $ω$ is absolutely continuous with respect to $H^{n}$, then $ω|_E$ is concentrated on an $n$-rectifiable set.

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Jonas Azzam, Mihalis Mourgoglou, Xavier Tolsa. 2015-05-29. Rectifiability of harmonic measure in domains with porous boundaries. https://arxiv.org/abs/1505.06088

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