Tangent measures and absolute continuity of harmonic measure

  1. Jonas Azzam 1
  2. Mihalis Mourgoglou 1
  1. 1 Universitat Autònoma de Barcelona
    info

    Universitat Autònoma de Barcelona

    Barcelona, España

    ROR https://ror.org/052g8jq94

Journal:
Revista matemática iberoamericana

ISSN: 0213-2230

Year of publication: 2018

Volume: 34

Issue: 1

Pages: 305-330

Type: Article

DOI: 10.4171/RMI/986 DIALNET GOOGLE SCHOLAR

More publications in: Revista matemática iberoamericana

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 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.

Data source: Dialnet