Mutual absolute continuity of interior and exterior harmonic measure implies rectifiability
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math.APmath.MG
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absolutecontinuityboundariesharmonicimpliesmeasuremutualrectifiability
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We show that, for disjoint domains in the Euclidean space whose boundaries satisfy a non-degeneracy condition, mutual absolute continuity of their harmonic measures implies absolute continuity with respect to surface measure and rectifiability in the intersection of their boundaries.
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