English

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