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

zbMath1319.53008arXiv1211.4912MaRDI QIDQ2341658

Masaaki Umehara, Wayne Rossman, Heayong Shin, Seong-Deog Yang, Sung-Eun Koh, Young Wook Kim, Kotaro Yamada, Shoichi Fujimori

Publication date: 27 April 2015

Published in: Osaka Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.4912

zbMATH Keywords

singular settype changespace-like maximal surfacestime-like minimal surfaces

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) PDEs of mixed type (35M10) Non-Euclidean differential geometry (53A35) Local differential geometry of Lorentz metrics, indefinite metrics (53B30)

Related Items (14)

Geometry of lightlike locus on mixed type surfaces in Lorentz-Minkowski 3-space from a contact viewpoint ⋮ Retraction note to: ``Extremal surface with the light-like line in Minkowski space \(R^{1+(1+1)}\) ⋮ Classification of zero mean curvature surfaces of separable type in Lorentz-Minkowski space ⋮ Swallowtails and cone-like singularities on a maxface ⋮ 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 ⋮ 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 \(\mathbb{R}^{1+(1+1)}\) ⋮ Zero mean curvature surfaces in \(\mathrm{L}^3\) containing a light-like line ⋮ Erratum to: ``Zero mean curvature surfaces in Lorentz-Minkowki 3-space which change type across a light-like line ⋮ Mixed type surfaces with bounded Gaussian curvature in three-dimensional Lorentzian manifolds ⋮ Hypersurfaces with light-like points in a Lorentzian manifold

Cites Work

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• Maximal surfaces in the 3-dimensional Minkowski space \(L^ 3\)
• Embedded triply periodic zero mean curvature surfaces of mixed type in Lorentz-Minkowski 3-space
• 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 in Lorentz-Minkowski 3-space and 2-dimensional fluid mechanics

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