%0 Journal Article
%T Uniform Rectifiability and harmonic measure IV: Ahlfors regularity plus Poisson kernels in $L^p$ implies uniform rectifiability
%A Steve Hofmann
%A J. M. Martell
%J Mathematics
%D 2015
%I arXiv
%X 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 $\Omega:= \mathbb{R}^{n+1}\setminus E$, implies uniform rectifiability of $E$.
%U http://arxiv.org/abs/1505.06499v1