Uniform rectifiability and harmonic measure, II: Poisson kernels in Lp imply uniform rectifiability
Uniform rectifiability and harmonic measure, II: Poisson kernels in Lp imply uniform rectifiability
We present the converse to a higher-dimensional, scale-invariant version of the classical F. and M. Riesz theorem, proved by the first two authors. More precisely, for n≥2, for an Ahlfors–David regular domain Ω⊂Rn+1 which satisfies the Harnack chain condition plus an interior (but not exterior) corkscrew condition, we show that …