Extensions of Calabi's correspondence between minimal surfaces and maximal surfaces
Differential Geometry
2011-04-20 v2 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.1103.5180,
title = {Extensions of Calabi's correspondence between minimal surfaces and maximal surfaces},
author = {Hojoo Lee},
journal= {arXiv preprint arXiv:1103.5180},
year = {2011}
}
Comments
31 pages