Dimension Drop for Harmonic Measure on Ahlfors Regular Boundaries
Dimension Drop for Harmonic Measure on Ahlfors Regular Boundaries
复制标题
Ahlfors 正则边界上谐波测量的降维
DOI：
10.1007/s11118-019-09796-6
复制
发表时间：
2018
影响因子：
1.1
通讯作者：
Jonas Azzam
中科院分区：
文献类型：
--
作者：
Jonas Azzam
We show that given a domain Ω⊆ℝd+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\Omega }\subseteq \mathbb {R}^{d+1}$\end{document} with uniformly non-flat Ahlfors s-regular boundary with s ≥ d, the dimension of its harmonic measure is strictly less than s.
We show that given a domain Ω⊆ℝd+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\Omega }\subseteq \mathbb {R}^{d+1}$\end{document} with uniformly non-flat Ahlfors s-regular boundary with s ≥ d, the dimension of its harmonic measure is strictly less than s.