Zero mean curvature surfaces in \(\mathrm{L}^3\) containing a light-like line

DOI10.1016/J.CRMA.2012.10.024zbMath1257.53090OpenAlexW2084060190MaRDI QIDQ694691

M. C. Fu

Publication date: 13 December 2012

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2012.10.024

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Local differential geometry of Lorentz metrics, indefinite metrics (53B30)

Related Items (17)

Retraction note to: ``Extremal surface with the light-like line in Minkowski space \(R^{1+(1+1)}\) ⋮ Quadrics and Scherk towers ⋮ Analytic extensions of constant mean curvature one geometric catenoids in de Sitter 3-space ⋮ Classification of zero mean curvature surfaces of separable type in Lorentz-Minkowski space ⋮ Space-like maximal surfaces containing entire null lines in Lorentz-Minkowski 3-space ⋮ Wick rotations of solutions to the minimal surface equation, the zero mean curvature equation and the Born-Infeld equation ⋮ On associate families of spacelike Delaunay surfaces ⋮ Embedded triply periodic zero mean curvature surfaces of mixed type in Lorentz-Minkowski 3-space ⋮ Reflection principle for lightlike line segments on maximal surfaces ⋮ CAUSAL CHARACTERS OF ZERO MEAN CURVATURE SURFACES OF RIEMANN TYPE IN THE LORENTZ-MINKOWSKI 3-SPACE ⋮ Extremal surface with the light-like line in Minkowski space \(\mathbb{R}^{1+(1+1)}\) ⋮ Existence and Regularity for Prescribed Lorentzian Mean Curvature Hypersurfaces, and the Born–Infeld Model ⋮ Improvement of the Bernstein-type theorem for space-like zero mean curvature graphs in Lorentz-Minkowski space using fluid mechanical duality ⋮ Mixed type surfaces with bounded Gaussian curvature in three-dimensional Lorentzian manifolds ⋮ Hypersurfaces with light-like points in a Lorentzian manifold ⋮ Zero mean curvature surfaces in Lorentz-Minkowski 3-space which change type across a light-like line ⋮ Global weak and smooth solutions of the equation for timelike extremal surface in Minkowski space

Cites Work

• Timelike minimal surfaces via loop groups
• Maximal surfaces in the 3-dimensional Minkowski space \(L^ 3\)
• Zero mean curvature surfaces in Lorentz-Minkowski 3-space which change type across a light-like line
• Prescribing singularities of maximal surfaces via a singular Björling representation formula
• Maximal surfaces with singularities in Minkowski space
• New maximal surfaces in Minkowski 3-space with arbitrary genus and their cousins in de Sitter 3-space
• SPACELIKE MAXIMAL SURFACES, TIMELIKE MINIMAL SURFACES, AND BJÖRLING REPRESENTATION FORMULAE
• A family of maximal surfaces in Lorentz-Minkowski three-space
• The extremal surfaces in the 3-dimensional Minkowski space
• Generalized maximal surfaces in Lorentz–Minkowski space L³
• Zero mean curvature surfaces of mixed type in Minkowski space

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