Harmonic measure is rectifiable if it is absolutely continuous with respect to the co-dimension-one Hausdorff measure

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

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

In the present paper, we sketch the proof of the fact that for any open connected set Ω⊂Rn+1, n≥1, and any E⊂∂Ω with 0<Hn(E)<∞, absolute continuity of the harmonic measure ω with respect to the Hausdorff measure on E implies that ωE is rectifiable.

Original languageEnglish (US)
Pages (from-to)351-355
Number of pages5
JournalComptes Rendus Mathematique
Volume354
Issue number4
DOIs
StatePublished - Apr 1 2016

Bibliographical note

Publisher Copyright:
© 2016 Académie des sciences.

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