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Constant mean curvature surfaces in Euclidean three-space. (English) Zbl 0636.53010

The author sketches a proof of the following results: any orientable compact surface of genus \(g\geq 3\) admits infinitely many immersions into E 3 with constant mean curvature. A non-compact surface of finite topological type with genus \(g\geq 0\) and \(m\geq 0\) ends or \(g\geq 2\) and \(m=2\) admits infinitely many proper immersions (often embeddings) with constant mean curvature into E 3. See also W. H. Meeks [Bull. Am. Math. Soc. 17, 315-317 (1987; Zbl 0634.53005)] where restrictions on the geometry of such surfaces are given.
Reviewer: G.Thorbergsson

MSC:

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

Citations:

Zbl 0634.53005
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References:

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