Rectifiability of harmonic measure

被引：53

作者：

Azzam, Jonas ^{[1
]}

Hofmann, Steve ^{[2
]}

Martell, Jose Maria ^{[3
]}

Mayboroda, Svitlana ^{[4
]}

Mourgoglou, Mihalis ^{[5
,6
]}

Tolsa, Xavier ^{[7
,8
]}

Volberg, Alexander ^{[9
]}

机构：

[1] Univ Autonoma Barcelona, Dept Matemat, Edifici C Fac Ciencies, Bellaterra 08193, Barcelona, Spain

[2] Univ Missouri, Dept Math, Columbia, MO 65211 USA

[3] UCM, Inst Ciencias Matemat, CSIC, UAM,UC3M, C Nicolas Cabrera 13-15, Madrid 28049, Spain

[4] Univ Minnesota, Dept Math, Minneapolis, MN 55455 USA

[5] Univ Autonoma Barcelona, Dept Matemat, Edifici C Fac Ciencies, Catalonia 08193, Barcelona, Spain

[6] Ctr Recerca Matemat, Edifici C Fac Ciencies, Catalonia 08193, Barcelona, Spain

[7] Univ Autonoma Barcelona, ICREA, Edifici C Fac Ciencies, Catalonia 08193, Barcelona, Spain

[8] BGSMath, Dept Matemat, Edifici C Fac Ciencies, Catalonia 08193, Barcelona, Spain

[9] Michigan State Univ, Dept Math, E Lansing, MI 48824 USA

来源：

GEOMETRIC AND FUNCTIONAL ANALYSIS | 2016年 / 26卷 / 03期

基金：

美国国家科学基金会; 欧洲研究理事会;

关键词：

BOUNDARY HARNACK PRINCIPLE; UNIFORM RECTIFIABILITY; HAUSDORFF DIMENSION; RIESZ TRANSFORM; HYPERSURFACES; SETS;

D O I：

10.1007/s00039-016-0371-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the present paper we prove that for any open connected set , , and any with , absolute continuity of the harmonic measure with respect to the Hausdorff measure on E implies that 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.

引用

页码：703 / 728

页数：26

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