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

doi:10.1016/j.crma.2016.01.012

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

Mathematics

Research output: Contribution to journal › Article › peer-review

3 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 ω_E is rectifiable.

Original language	English (US)
Pages (from-to)	351-355
Number of pages	5
Journal	Comptes Rendus Mathematique
Volume	354
Issue number	4
DOIs	https://doi.org/10.1016/j.crma.2016.01.012
State	Published - Apr 1 2016

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© 2016 Académie des sciences.

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AU - Mourgoglou, Mihalis

AU - Tolsa, Xavier

AU - Volberg, Alexander

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

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