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Uniqueness of the Riemann minimal examples. (English) Zbl 0916.53004

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.

MSC:

53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
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