Mathematics – Differential Geometry
Scientific paper
2011-03-27
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.
Lee Hojoo
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