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Uniform domain and max-min inequality property. (Chinese. English summary) Zbl 1199.30127

Summary: Introducing the max-min inequality property of domain, we investigate the relation between uniform domain and max-min inequality property, and obtain the following results: (1) if \(D\) is uniform domain, then \(D\) has max-min inequality property; (2) if \(D\subset \overline{\mathbb{R}}^2\) and \(D^*=\overline{\mathbb{R}}^2\backslash \overline{D}\) have max-min inequality property, respectively, then \(D\) is uniform domain.

MSC:

30C62 Quasiconformal mappings in the complex plane
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