QED domains and NED sets in \overline{𝐑}ⁿ

Yang, Shan Shuang

doi:10.1090/S0002-9947-1992-1065605-6

QED domains and NED sets in $\mathbf {\overline {R}}^ n$
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Trans. Amer. Math. Soc. 334 (1992), 97-120 Request permission

Abstract:

This paper contributes to the theory of quasiextremal distance (or ${\text {QED}}$) domains. We associate with every ${\text {QED}}$ domain $D$ two ${\text {QED}}$ constants $M(D)$ and ${M^{\ast } }(D)$ and exhibit how these constants reflect the geometry of $D$. For example, we give a geometric characterization for ${\text {QED}}$ domains $D$ with ${M^{\ast }}(D) = 2$ and obtain some sharp estimates of ${\text {QED}}$ constants $M(D)$ and ${M^{\ast } }(D)$ for different kinds of domains.

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