Extensions of Calabi's correspondence between minimal surfaces and   maximal surfaces
  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. 
Hojoo Lee
math.DG math-ph math.AP math.MP