Lopez, Francisco J.; Ros, Antonio On embedded complete minimal surfaces of genus zero. (English) Zbl 0719.53004 J. Differ. Geom. 33, No. 1, 293-300 (1991). The authors prove that the Riemann sphere \(S^ 2\) punctured at N points, \(N\geq 3\), cannot be embedded in \({\mathbb{R}}^ 3\) as a complete minimal surface with finite total curvature. This important result together with the works of R. Osserman [Ann. Math., II. Ser. 80, 340-364 (1964; Zbl 0134.385)] and of L. Jorge and W. Meeks [Topology 22, 203-221 (1983; Zbl 0517.53008)] show that the plane and the catenoid are the only embedded complete minimal surfaces of finite total curvature and genus zero in \({\mathbb{R}}^ 3\). Reviewer: C.J.Costa (Niteroi) Cited in 1 ReviewCited in 53 Documents MSC: 53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature Keywords:complete minimal surface; finite total curvature; genus zero Citations:Zbl 0134.385; Zbl 0517.53008 PDFBibTeX XMLCite \textit{F. J. Lopez} and \textit{A. Ros}, J. Differ. Geom. 33, No. 1, 293--300 (1991; Zbl 0719.53004) Full Text: DOI