Rectifiability of harmonic measure in domains with porous boundaries

Jonas Azzam, Mihalis Mourgoglou, Xavier Tolsa

We show that if $n\ge 1$, $\Omega \subset {\mathbb{R}}^{n+1}$ is a connected domain with porous boundary, and $E\subset \partial \Omega$ is a set of finite and positive Hausdorff $H^n$-measure…