Zero mean curvature entire graphs of mixed type in Lorentz-Minkowski 3-space

2015/11/25 by Shoichi Fujimori, Fujimori, Shoichi, Yu Kawakami +9
Mathematics · Physics and Astronomy · #53A10 (Primary) #53A35 #53C50 (Secondary) #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.1511.07954

openalex publication_date 2015/11/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

It is classically known that the only zero mean curvature entire graphs in the Euclidean 3-space are planes, by Bernstein's theorem. A surface in Lorentz-Minkowski 3-space \boldsymbolR³₁ is called of mixed type if it changes causal type from space-like to time-like. In \boldsymbolR³₁, Osamu Kobayashi found two zero mean curvature entire graphs of mixed type that are not planes. As far as the authors know, these two examples were the only known examples of entire zero mean curvature graphs of mixed type without singularities. In this paper, we construct several families of real analytic zero mean curvature entire graphs of mixed type in Lorentz-Minkowski 3-space. The entire graphs mentioned above lie in one of these classes.

Citations

• Mixed type surfaces with bounded mean curvature in 3-dimensional space-times

Cited by

• Fold singularities on spacelike CMC surfaces in Lorentz-Minkowski space
• Causal characters of zero mean curvature surfaces of Riemann type in the Lorentz-Minkowski 3-space

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