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Minimal surfaces based on the catenoid. (English) Zbl 0737.53006

From the paper: “In this article, we have tried to give a survey of some recent progress in the theory of minimal surfaces, while at the same time illustrating some of the underlying techniques and stressing the connection with the classical point of view”.
The authors talk about complete embedded minimal surfaces and its construction when the surface has finite total curvature or is periodic. All minimal surfaces foliated by convex curves in parallel planes are discussed. This is similar to Schiffman’s results about minimal annuli and Riemann’s examples. The references include important contributions in those directions and are a good starting point for beginners.

MSC:

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