Liao, Maoxin; Chu, Yuming; Li, Xianyi Uniform domain and max-min inequality property. (Chinese. English summary) Zbl 1199.30127 Acta Math. Sci., Ser. A, Chin. Ed. 29, No. 1, 121-126 (2009). 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 Keywords:uniform domain; max-min inequality property; quasiconformal mappings; weakly Cigar domain; quasi-invariance; hyperbolic geodesic PDFBibTeX XMLCite \textit{M. Liao} et al., Acta Math. Sci., Ser. A, Chin. Ed. 29, No. 1, 121--126 (2009; Zbl 1199.30127)