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

Abstract

The main goal of this survey is to illustrate geometric applications of the Poincaré 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.

31 pages

References in corpus (2)

• Calabi-Bernstein results for maximal surfaces in Lorentzian product spaces
• A uniqueness result for maximal surfaces in Minkowski 3-space