Singular Sets for Harmonic Measure on Locally Flat Domains with Locally Finite Surface Measure
نویسندگان
چکیده
منابع مشابه
Singular Sets for Harmonic Measure on Locally Flat Domains with Locally Finite Surface Measure
A theorem of David and Jerison asserts that harmonic measure is absolutely continuous with respect to surface measure in NTA domains with Ahlfors regular boundaries. We prove that this fails in high dimensions if we relax the Ahlfors regularity assumption by showing that, for each d > 1, there exists a Reifenberg flat domain Ω ⊂ R with H(∂Ω) < ∞ and a subset E ⊂ ∂Ω with positive harmonic measur...
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ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2016
ISSN: 1073-7928,1687-0247
DOI: 10.1093/imrn/rnw121