A Calabi's Type Correspondence

2019/01/31 by Martínez, Antonio, Triviño, A. L. Martínez · 1 citation
#35J60 #53C42 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1901.11451

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 \mathbbL³. 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.

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