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arXiv · 1901.11451

A Calabi's Type Correspondence

Antonio Martínez·A. L. Martínez Triviño
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Abstract

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.

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Antonio Martínez, A. L. Martínez Triviño. 2019-01-31. A Calabi's Type Correspondence. https://arxiv.org/abs/1901.11451

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