Zero mean curvature surfaces in Lorentz-Minkowski 3-space which change type across a light-like line

2012/11/21 by Shoichi Fujimori, Fujimori, Shoichi, Young‐Wook Kim +13
Mathematics · Physics and Astronomy · #53A10 (Primary) 53B30 (Secondary) #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1211.4912

openalex publication_date 2012/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is well-known that space-like maximal surfaces and time-like minimal surfaces in Lorentz-Minkowski 3-space R³₁ have singularities in general. They are both characterized as zero mean curvature surfaces. We are interested in the case where the singular set consists of a light-like line, since this case has not been analyzed before. As a continuation of a previous work by the authors, we give the first example of a family of such surfaces which change type across the light-like line. As a corollary, we also obtain a family of zero mean curvature hypersurfaces in Rⁿ⁺¹₁ that change type across an (n-1)-dimensional light-like plane.

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