Meeks, William H. III; Pérez, Joaquín; Ros, Antonio Uniqueness of the Riemann minimal examples. (English) Zbl 0916.53004 Invent. Math. 133, No. 1, 107-132 (1998). Riemann classified all minimal surfaces in \(\mathbb{R}^3\) that are foliated by circles and straight lines in horizontal planes. The only such surfaces are the plane, the helicoid, and a one-parameter family of what are now called Riemann minimal examples. In the paper under review, the authors show that the only properly embedded periodic minimal surfaces in \(\mathbb{R}^3\) of genus zero with two limit ends are the Riemann minimal examples. Reviewer: T.Hasanis (Ioannina) Cited in 4 ReviewsCited in 12 Documents MSC: 53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature Keywords:Euclidean 3-space; periodic minimal surfaces; genus zero; limit ends PDFBibTeX XMLCite \textit{W. H. Meeks III} et al., Invent. Math. 133, No. 1, 107--132 (1998; Zbl 0916.53004) Full Text: DOI