Rectifiability of harmonic measure

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

doi:10.1007/s00039-016-0371-x

Rectifiability of harmonic measure

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

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	703-728
Number of pages	26
Journal	Geometric and Functional Analysis
Volume	26
Issue number	3
DOIs	https://doi.org/10.1007/s00039-016-0371-x
Publication status	Published - 16 Jun 2016
Externally published	Yes

Access to Document

10.1007/s00039-016-0371-x

https://arxiv.org/abs/1509.06294

Cite this

@article{9288a60f37814e58a019cb43b922717f,

title = "Rectifiability of harmonic measure",

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.",

author = "Jonas Azzam and Steve Hofmann and Martell, {Jose Maria} and Svitlana Mayboroda and Mihalis Mourgoglou and Xavier Tolsa and Alexander Volberg",

year = "2016",

month = jun,

day = "16",

doi = "10.1007/s00039-016-0371-x",

language = "English",

volume = "26",

pages = "703--728",

journal = "Geometric and Functional Analysis",

issn = "1016-443X",

publisher = "Birkhauser Verlag Basel",

number = "3",

}

TY - JOUR

T1 - Rectifiability of harmonic measure

AU - Azzam, Jonas

AU - Hofmann, Steve

AU - Martell, Jose Maria

AU - Mayboroda, Svitlana

AU - Mourgoglou, Mihalis

AU - Tolsa, Xavier

AU - Volberg, Alexander

PY - 2016/6/16

Y1 - 2016/6/16

N2 - 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.

AB - 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.

U2 - 10.1007/s00039-016-0371-x

DO - 10.1007/s00039-016-0371-x

M3 - Article

SN - 1016-443X

VL - 26

SP - 703

EP - 728

JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

IS - 3

ER -

Rectifiability of harmonic measure

Abstract

Access to Document

Fingerprint

Cite this