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- Title
Tangent measures and absolute continuity of harmonic measure.
- Authors
Azzam, Jonas; Mourgoglou, Mihalis
- Abstract
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 nondegenerate 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.
- Subjects
TANGENTS (Geometry); HAUSDORFF spaces; ABSOLUTE continuity; HARMONIC analysis (Mathematics); NON-degenerate perturbation theory
- Publication
Revista Mathematica Iberoamericana, 2018, Vol 34, Issue 1, p305
- ISSN
0213-2230
- Publication type
Article
- DOI
10.4171/RMI/986