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arXiv · 1509.06558

Harmonic measure is rectifiable if it is absolutely continuous with respect to the co-dimension one Hausdorff measure

Jonas Azzam·Steve Hofmann·José María Martell·Svitlana Mayboroda·Mihalis Mourgoglou·Xavier Tolsa·Alexander Volberg
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Abstract

In the present paper we sketch the proof of the fact that for any open connected set $\Omega\subset\mathbb{R}^{n+1}$, $n\geq 1$, and any $E\subset \partial \Omega$ with $0<\mathcal{H}^n(E)<\infty$, absolute continuity of the harmonic measure $\omega$ with respect to the Hausdorff measure on $E$ implies that $\omega|_E$ is rectifiable.

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Jonas Azzam, Steve Hofmann, José María Martell, Svitlana Mayboroda, Mihalis Mourgoglou, Xavier Tolsa, Alexander Volberg. 2015-09-22. Harmonic measure is rectifiable if it is absolutely continuous with respect to the co-dimension one Hausdorff measure. https://doi.org/10.1016/j.crma.2016.01.012

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