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arXiv · 1505.06499

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

Steve Hofmann·J. M. Martell
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Abstract

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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Steve Hofmann, J. M. Martell. 2015-05-24. Uniform Rectifiability and harmonic measure IV: Ahlfors regularity plus Poisson kernels in $L^p$ implies uniform rectifiability. https://arxiv.org/abs/1505.06499

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