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

Zeitschrift:
Revista matemática iberoamericana

ISSN: 0213-2230

Datum der Publikation: 2018

Ausgabe: 34

Nummer: 1

Seiten: 305-330

Art: Artikel

DOI: 10.4171/RMI/986 DIALNET GOOGLE SCHOLAR

Andere Publikationen in: Revista matemática iberoamericana

Zusammenfassung

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.

Fuente de los datos: Dialnet