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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.

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