Mutual absolute continuity of interior and exterior harmonic measure\n implies rectifiability

2016/02/03 by Jonas Azzam, Mihalis Mourgoglou, Azzam, Jonas +3 · 2 citations
Computer Science · Mathematics · #28A75 #28A78 #31A15 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Metric Geometry (math.MG) #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1602.01397

openalex publication_date 2016/02/03 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

We show that, for disjoint domains in the Euclidean space whose boundaries\nsatisfy a non-degeneracy condition, mutual absolute continuity of their\nharmonic measures implies absolute continuity with respect to surface measure\nand rectifiability in the intersection of their boundaries.\n

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