Rectifiability of harmonic measure

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

Research output: Contribution to journalArticlepeer-review

38 Scopus citations

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 (US)
Pages (from-to)703-728
Number of pages26
JournalGeometric and Functional Analysis
Volume26
Issue number3
DOIs
StatePublished - Jun 1 2016

Bibliographical note

Publisher Copyright:
© 2016, Springer International Publishing.

Fingerprint

Dive into the research topics of 'Rectifiability of harmonic measure'. Together they form a unique fingerprint.

Cite this