Extensions of Calabi's correspondence between minimal surfaces and maximal surfaces

2011/03/27 by Hojoo Lee, Lee, Hojoo
Mathematics · Physics and Astronomy · #35J47 #35J60 #49Q05 #53C50 #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.1103.5180

openalex publication_date 2011/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The main goal of this survey is to illustrate geometric applications of the Poincaré Lemma to constant mean curvature equations. In 1970, Calabi introduced the duality between minimal graphs in three dimensional Euclidean space and maximal graphs in three dimensional Lorentz space. We construct two extensions of Calabi's correspondence.

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