Rectifiability of harmonic measure

Jonas Azzam, Steve Hofmann, José María Martell, Svitlana Mayboroda, Mihalis Mourgoglou, Xavier Tolsa, Alexander Volberg

Research output: Contribution to journalArticleResearchpeer-review

28 Citations (Scopus)

Abstract

© 2016, Springer International Publishing. In the present paper we prove that for any open connected set Ω ⊂ Rn+1, n≥ 1 , and any E⊂ ∂Ω with Hn(E) < ∞, absolute continuity of the harmonic measure ω with respect to the Hausdorff measure on E implies that ω| E is rectifiable. This solves an open problem on harmonic measure which turns out to be an old conjecture even in the planar case n= 1.
Original languageEnglish
Pages (from-to)703-728
JournalGeometric and Functional Analysis
Volume26
Issue number3
DOIs
Publication statusPublished - 1 Jun 2016

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