A Calabi's Type Correspondence
Calabi observed that there is a natural correspondence between the solutions of the minimal surface equation in $\mathbb{R}^3$ with those of the maximal spacelike surface equation in $\mathbb{L}^3$. We are going to show how this correspondence can be extended to the family of $φ$-minimal graphs in $\mathbb{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.
math.DG↗