Harmonic measure and approximation of uniformly rectifiable sets
Harmonic measure and approximation of uniformly rectifiable sets
复制标题
一致可整流集的谐波测度和近似
DOI：
10.4171/rmi/940
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
S. Hofmann
中科院分区：
文献类型：
--
作者：
S. Bortz;S. Hofmann
令$E\subset \mathbb{R}^{n+1}$，$n\ge 1$，是维度$n$的一致可求长集。我们显示$E$，有大片的边界的一类域，满足2侧螺旋形条件，其连接组件都是弦弧域（与统一控制的各种常数）。由此，我们推论出E$有大片集的调和测度属于弱-A\infty$
Let $E\subset \mathbb{R}^{n+1}$, $n\ge 1$, be a uniformly rectifiable set of dimension $n$. We show $E$ that has big pieces of boundaries of a class of domains which satisfy a 2-sided corkscrew condition, and whose connected components are all chord-arc domains (with uniform control of the various constants). As a consequence, we deduce that $E$ has big pieces of sets for which harmonic measure belongs to weak-$A_\infty$