Dimension drop for harmonic measure on Ahlfors regular boundaries

Jonas Azzam

Dimension drop for harmonic measure on Ahlfors regular boundaries

Classical Analysis and ODEs 2019-06-26 v3 Analysis of PDEs Metric Geometry

Authors: Jonas Azzam

Abstract

We show that given a domain $\Omega\subseteq \mathbb{R}^{d+1}$ with uniformly non-flat Ahlfors $s$ -regular boundary and $s\geq d$ , the dimension of its harmonic measure is strictly less than $s$ .

Keywords

bounded domains hausdorff measure and dimension harmonic functions

Cite

@article{arxiv.1811.03769,
  title  = {Dimension drop for harmonic measure on Ahlfors regular boundaries},
  author = {Jonas Azzam},
  journal= {arXiv preprint arXiv:1811.03769},
  year   = {2019}
}

Comments

Corrected typos and mistakes (in particular, a part of Lemma 4.1 was poorly written), made minor corrections to statements of Lemma 4.1 and Lemma 4.2, amended introduction slightly, added a figure. To appear in Potential Analysis

Dimension drop for harmonic measure on Ahlfors regular boundaries

Abstract

Keywords

Cite

Comments

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