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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

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.

MSC:

53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
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