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

Abstract

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

arXiv admin note: text overlap with arXiv:1509.06294