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A Calabi's Type Correspondence. (arXiv:1901.11451v1 [math.DG])

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 $\varphi $-minimal graphs in $\mathbb{R}^3 $ when the function $\varphi$ is invariant under a two-parametric group of translations. We give also applications in the study and description of new examples.查看全文

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