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

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
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### References:

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