Absolute continuity between the surface measure and harmonic measure implies rectifiability

Steve Hofmann, José Maria Martell, Svitlana Mayboroda +2

In the present paper we prove that for any open connected set $\Omega \subset {\mathbb{R}}^{n+1}$, $n\ge 1$, and any $E\subset \partial \Omega$ with $0<{\mathcal{H}}^n(E)<\infty$ absolute contin…