Singularities of Maximal Surfaces

2005/10/18 by Shoichi Fujimori, Fujimori, Shoichi, Kentaro Saji +5 · 4 citations
Mathematics · Medicine · #53A10 #53B30 #57R45 #Advanced Neuroimaging Techniques and Applications #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.math/0510366

openalex publication_date 2005/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the singularities of spacelike maximal surfaces in Lorentz-Minkowski 3-space generically consist of cuspidal edges, swallowtails and cuspidal cross caps. The same result holds for spacelike mean curvature one surfaces in de Sitter 3-space. To prove these, we shall give a simple criterion for a given singular point on a surface to be a cuspidal cross cap.

Cited by

• Singularities of translation surfaces under the linearly dependent condition in Euclidean 3-space
• Discrete minimal surfaces: Old and New
• A class of affine maximal surfaces with singularities and its relationship with minimal surface theory
• Geometry on the Gluing Locus of Two Surfaces

Related

• Maximal surfaces with singularities in Minkowski space
• Cuspidal edges and generalized cuspidal edges in the Lorentz-Minkowski 3-space
• Singularities of generalized timelike minimal surfaces in Lorentz-Minkowski 3-space
• Fold singularities on spacelike CMC surfaces in Lorentz-Minkowski space
• Singularities of spacelike mean curvature one surfaces in de Sitter space