A Calabi’s type correspondence

Abstract Calabi observed that there is a natural correspondence between the solutions of the minimal surface equation in R 3 with those of the maximal spacelike surface equation in L 3 . We are going to show how this correspondence can be extended to the family of φ -minimal graphs in R 3 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.