TY - JOUR

T1 - Harmonic measure is rectifiable if it is absolutely continuous with respect to the co-dimension-one Hausdorff measure

AU - Azzam, Jonas

AU - Hofmann, Steve

AU - Martell, José María

AU - Mayboroda, Svitlana

AU - Mourgoglou, Mihalis

AU - Tolsa, Xavier

AU - Volberg, Alexander

PY - 2016/4/1

Y1 - 2016/4/1

N2 - © 2016 Académie des sciences. 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.

AB - © 2016 Académie des sciences. 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.

U2 - 10.1016/j.crma.2016.01.012

DO - 10.1016/j.crma.2016.01.012

M3 - Article

SN - 1631-073X

VL - 354

SP - 351

EP - 355

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 4

ER -