The weak-$A_{\infty }$ property of harmonic and $p$-harmonic measures implies uniform rectifiability

Steve Hofmann, Phi Le, José María Martell +1

Let $E\subset {\mathbb{R}}^{n+1}$, $n\ge 2$, be an Ahlfors-David regular set of dimension $n$. We show that the weak-$A_{\infty }$ property of harmonic measure, for the open set $Ω:= \m…