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

@article{Hofmann2015UniformRA, title={Uniform Rectifiability and harmonic measure IV: Ahlfors regularity plus Poisson kernels in \$L^p\$ implies uniform rectifiability}, author={Steve Hofmann and Jos'e Mar'ia Martell}, journal={arXiv: Classical Analysis and ODEs}, year={2015} }

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 $E$.

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