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

摘要

In the present paper, we sketch the proof of the fact that for any open connected set Omega subset of Rn+1, n >= 1, and any E subset of partial derivative Omega with 0 < H-n(E) < infinity, absolute continuity of the harmonic measure omega with respect to the Hausdorff measure on E implies that omega vertical bar(E) is rectifiable. (C) 2016 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.