Let , , be an Ahlfors–David regular set of dimension . We show that the weak- property of harmonic measure, for the open set , implies uniform rectifiability of . More generally, we establish a similar result for the Riesz measure, -harmonic measure, associated to the -Laplace operator, .
"The weak-$A_\infty$ property of harmonic and $p$-harmonic measures implies uniform rectifiability." Anal. PDE 10 (3) 513 - 558, 2017. https://doi.org/10.2140/apde.2017.10.513