Lazard-Holly, Hippolyte; Meeks, William H. III Classification of genus zero minimal surfaces properly embedded in \(\mathbb{R}^ 3/\mathbb{Z}^ 2\). (Classification des surfaces minimales de genre zéro proprement plongées dans \(\mathbb{R}^ 3/\mathbb{Z}^ 2\).) (French) Zbl 0884.53046 C. R. Acad. Sci., Paris, Sér. I, Math. 325, No. 7, 753-754 (1997). Summary: We prove that every genus zero minimal surface properly embedded in a flat manifold \(\mathbb{R}^3/ \Lambda\), where \(\Lambda\) is a lattice generated by two independent translations, must be a quotient of a doubly-periodic Scherk surface. Cited in 1 ReviewCited in 1 Document MSC: 53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) 53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature Keywords:classification; genus zero minimal surfaces; doubly-periodic Scherk surface PDFBibTeX XMLCite \textit{H. Lazard-Holly} and \textit{W. H. Meeks III}, C. R. Acad. Sci., Paris, Sér. I, Math. 325, No. 7, 753--754 (1997; Zbl 0884.53046) Full Text: DOI