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arXiv · 1507.04409

Absolute continuity between the surface measure and harmonic measure implies rectifiability

Steve Hofmann·José Maria Martell·Svitlana Mayboroda·Xavier Tolsa·Alexander Volberg
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Abstract

In the present paper we prove 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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Steve Hofmann, José Maria Martell, Svitlana Mayboroda, Xavier Tolsa, Alexander Volberg. 2015-07-15. Absolute continuity between the surface measure and harmonic measure implies rectifiability. https://arxiv.org/abs/1507.04409

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