Rectifiability of harmonic measure

Jonas Azzam, Steve Hofmann, Jose Maria Martell, Svitlana Mayboroda, Mihalis Mourgoglou, Xavier Tolsa, Alexander Volberg

Research output: Contribution to journalArticlepeer-review

Abstract

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
Number of pages26
JournalGeometric and Functional Analysis
Volume26
Issue number3
DOIs
Publication statusPublished - 16 Jun 2016
Externally publishedYes

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