Extensions of Calabi's correspondence between minimal surfaces and maximal surfaces

Details Extensions of Calabi's correspondence between minimal surfaces and maximal surfaces Extensions of Calabi's correspondence between minimal surfaces and maximal surfaces

2011-03-27

arxiv.org/abs/1103.5180v2

Mathematics

Differential Geometry

31 pages

Scientific paper

The main goal of this survey is to illustrate geometric applications of the
Poincar\'{e} Lemma to constant mean curvature equations. In 1970, Calabi
introduced the duality between minimal graphs in three dimensional Euclidean
space and maximal graphs in three dimensional Lorentz space. We construct two
extensions of Calabi's correspondence.

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