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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

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


Author: Shan Shuang Yang
Journal: Trans. Amer. Math. Soc. 334 (1992), 97-120
MSC: Primary 30C65
DOI: https://doi.org/10.1090/S0002-9947-1992-1065605-6
MathSciNet review: 1065605
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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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DOI: https://doi.org/10.1090/S0002-9947-1992-1065605-6
Keywords: $ {\text{QED}}$ domain, $ {\text{NED}}$ set, modulus of a curve family, conformal capacity, quasiconformal mapping, quasiconformal reflection, quasicircle
Article copyright: © Copyright 1992 American Mathematical Society

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