Marginally trapped surfaces in \mathbbL⁴ and three Weierstrass representations

2022/02/20 by Hojoo Lee, Lee, Hojoo
Mathematics · Physics and Astronomy · #53A10 #53C42 #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2202.09800

openalex publication_date 2022/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct new integrable systems to present Weierstrass type representations for spacelike surfaces whose mean curvature vector H satisfies the null condition ⟨ H, H ⟩=0 in the four dimensional Lorentz-Minkowski space \mathbbL⁴. Our new Weierstrass presentations extend simultaneously classical Weierstrass representations (of the first kind and the second kind) for maximal surfaces in \mathbbL³ and minimal surfaces in ℝ³. We solve a linear partial differental equation to construct explicit examples of marginally trapped surfaces with nowhere vanishing mean curvature vector.

Related

• Marginally trapped surfaces in L4 and an extended Weierstrass-Bryant representation
• Weierstrass representation for timelike minimal surfaces in Minkowski 3-space
• A geometric study of marginally trapped surfaces in space forms and Robertson-Walker spacetimes -- an overview
• Canonical Weierstrass Representation of Minimal and Maximal Surfaces in the Three-dimensional Minkowski Space
• A note on the generalized Weierstrass representation