A Calabi’s type correspondence

Abstract

Calabi observed that there is a natural correspondence between the solutions of the minimal surface equation in R3 with those of the maximal spacelike surface equation in L3. We are going to show how this correspondence can be extended to the family of φ-minimal graphs in R3 when the function φ is invariant under a two-parametric group of translations. We give also applications in the study and description of new examples.