Uniform Rectifiability and harmonic measure IV: Ahlfors regularity plus Poisson kernels in $L^p$ implies uniform rectifiability

Steve Hofmann, J. M. Martell

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…