Mutual Absolute Continuity of Interior and Exterior Harmonic Measure Implies Rectifiability

Mutual Absolute Continuity of Interior and Exterior Harmonic Measure Implies Rectifiability

We show that, for disjoint domains in the euclidean space whose boundaries satisfy a nondegeneracy condition, mutual absolute continuity of their harmonic measures implies absolute continuity with respect to surface measure and rectifiability in the intersection of their boundaries. © 2017 Wiley Per...

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Veröffentlicht in:Communications on pure and applied mathematics 2017-11, Vol.70 (11), p.2121-2163
Hauptverfasser: Azzam, Jonas, Mourgoglou, Mihalis, Tolsa, Xavier
Format: Artikel
Sprache:eng
Schlagworte:
Boundaries
Continuity
Euclidean geometry
Euclidean space
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Zusammenfassung:We show that, for disjoint domains in the euclidean space whose boundaries satisfy a nondegeneracy condition, mutual absolute continuity of their harmonic measures implies absolute continuity with respect to surface measure and rectifiability in the intersection of their boundaries. © 2017 Wiley Periodicals, Inc.
ISSN:0010-3640
1097-0312
DOI:10.1002/cpa.21687