2024/08/01 by Shintaro Akamine, Akamine, Shintaro
Mathematics · Physics and Astronomy · #57R45 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Primary 53A10 #Secondary 53B30
paper · pdf · doi:10.48550/arxiv.2408.00313
openalex publication_date 2024/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A timelike minimal surface in Minkowski 3-space is a surface whose induced metric is Lorentzian and with vanishing mean curvature. Such surfaces have many kinds of singularities. In this paper, we prove existence and non-existence theorems of singularities of timelike minimal surfaces, and show that various diffeomorphism types of singularities that do not appear on these Riemannian counter parts, such as minimal surfaces in Euclidean space and maximal surfaces in Minkowski space, appear on timelike minimal surfaces. We also give criteria for cuspidal butterfly, cuspidal S1 singularity, (2,5)-cuspidal edge, cuspidal beaks and D4 singularity of timelike minimal surfaces. Finally, duality and invariance theorems for these singularities and examples are given.