Complete minimal surfaces with long line boundaries. (English) Zbl 0637.53007

Langevin, R.; Levitt, G.; Rosenberg, H.

Duke Math. J. 55, 985-995 (1987).

The authors prove Bernstein-type theorems for complete minimal surfaces bounded by lines in \({\mathbb{R}}^ 3.\) For example, if M is a complete minimal surface whose interior is a graph over a square J in the (x,y) plane, and if the boundary of M is composed of the four vertical lines over the vertices of J, then M is Scherk’s surface.

Reviewer: F.Gackstatter

MSC:

53A10

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature

Keywords:

Bernstein-type theorems; minimal surfaces

References:

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