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Complete embedded minimal surfaces of finite total curvature. (English) Zbl 0936.53006
Summary: A general construction, for complete embedded minimal surfaces of finite total curvature in Euclidean three-space, is carried out. In particular, examples with an arbitrary number of ends are given for the first time. The construction amounts to desingularizing the circles of intersection of a collection of coaxial catenoids and planes. The desingularization process uses Scherk’s singly periodic surfaces for an approximate construction which is subsequently corrected by singular perturbation methods.

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