Tangent measures and absolute continuity of harmonic measure
- Jonas Azzam 1
- Mihalis Mourgoglou 1
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1
Universitat Autònoma de Barcelona
info
ISSN: 0213-2230
Année de publication: 2018
Volumen: 34
Número: 1
Pages: 305-330
Type: Article
D'autres publications dans: Revista matemática iberoamericana
Résumé
We show that for uniform domains Ω⊆Rd+1 whose boundaries satisfy a certain nondegeneracy condition that harmonic measure cannot be mutually absolutely continuous with respect to α-dimensional Hausdorff measure unless α≤d. We employ a lemma that shows that, at almost every non-degenerate point, we may find a tangent measure of harmonic measure whose support is the boundary of yet another uniform domain whose harmonic measure resembles the tangent measure.