January & February  2009, 23(1&2): 341-365. doi: 10.3934/dcds.2009.23.341

Isometric immersions into the Minkowski spacetime for Lorentzian manifolds with limited regularity

1. 

Laboratoire Jacques-Louis Lions & Centre National de la Recherche Scientique, Université Pierre et Marie Curie (Paris 6), 4 Place Jussieu, 75252 Paris, France

2. 

Laboratoire Jacques-Louis Lions & Centre National de la Recherche Scientique, Universite Pierre et Marie Curie (Paris 6), 4 Place Jussieu, 75252 Paris

3. 

Institüt für Mathematik, Abt. Angewandte Mathematik, Universitüt Zürich, Winterthurerstrasse 190, 8057 Zürich, Swaziland

Received  November 2007 Revised  January 2008 Published  September 2008

Assuming minimal regularity assumptions on the data, we revisit the classical problem of finding isometric immersions into the Minkowski spacetime for hypersurfaces of a Lorentzian manifold. Our approach encompasses metrics having Sobolev regularity and Riemann curvature defined in the distributional sense, only. It applies to timelike, spacelike, or null hypersurfaces with arbitrary signature that possibly changes from point to point.
Citation: Philippe G. Lefloch, Cristinel Mardare, Sorin Mardare. Isometric immersions into the Minkowski spacetime for Lorentzian manifolds with limited regularity. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 341-365. doi: 10.3934/dcds.2009.23.341
[1]

Yiran Wang. Parametrices for the light ray transform on Minkowski spacetime. Inverse Problems & Imaging, 2018, 12 (1) : 229-237. doi: 10.3934/ipi.2018009

[2]

Xumin Jiang. Isometric embedding with nonnegative Gauss curvature under the graph setting. Discrete & Continuous Dynamical Systems - A, 2019, 39 (6) : 3463-3477. doi: 10.3934/dcds.2019143

[3]

Agust Sverrir Egilsson. On embedding the $1:1:2$ resonance space in a Poisson manifold. Electronic Research Announcements, 1995, 1: 48-56.

[4]

Aylin Aydoğdu, Sean T. McQuade, Nastassia Pouradier Duteil. Opinion Dynamics on a General Compact Riemannian Manifold. Networks & Heterogeneous Media, 2017, 12 (3) : 489-523. doi: 10.3934/nhm.2017021

[5]

Erwann Delay, Pieralberto Sicbaldi. Extremal domains for the first eigenvalue in a general compact Riemannian manifold. Discrete & Continuous Dynamical Systems - A, 2015, 35 (12) : 5799-5825. doi: 10.3934/dcds.2015.35.5799

[6]

Jian Zhai, Jianping Fang, Lanjun Li. Wave map with potential and hypersurface flow. Conference Publications, 2005, 2005 (Special) : 940-946. doi: 10.3934/proc.2005.2005.940

[7]

R. Bartolo, Anna Maria Candela, J.L. Flores. Timelike Geodesics in stationary Lorentzian manifolds with unbounded coefficients. Conference Publications, 2005, 2005 (Special) : 70-76. doi: 10.3934/proc.2005.2005.70

[8]

Randall Dougherty and Thomas Jech. Left-distributive embedding algebras. Electronic Research Announcements, 1997, 3: 28-37.

[9]

Miguel Ângelo De Sousa Mendes. Quasi-invariant attractors of piecewise isometric systems. Discrete & Continuous Dynamical Systems - A, 2003, 9 (2) : 323-338. doi: 10.3934/dcds.2003.9.323

[10]

Makoto Nakamura. Remarks on a dispersive equation in de Sitter spacetime. Conference Publications, 2015, 2015 (special) : 901-905. doi: 10.3934/proc.2015.0901

[11]

Andrea Natale, François-Xavier Vialard. Embedding Camassa-Holm equations in incompressible Euler. Journal of Geometric Mechanics, 2019, 11 (2) : 205-223. doi: 10.3934/jgm.2019011

[12]

Thais Bardini Idalino, Lucia Moura. Embedding cover-free families and cryptographical applications. Advances in Mathematics of Communications, 2019, 13 (4) : 629-643. doi: 10.3934/amc.2019039

[13]

Chuanqiang Chen. On the microscopic spacetime convexity principle for fully nonlinear parabolic equations II: Spacetime quasiconcave solutions. Discrete & Continuous Dynamical Systems - A, 2016, 36 (9) : 4761-4811. doi: 10.3934/dcds.2016007

[14]

Chuanqiang Chen. On the microscopic spacetime convexity principle of fully nonlinear parabolic equations I: Spacetime convex solutions. Discrete & Continuous Dynamical Systems - A, 2014, 34 (9) : 3383-3402. doi: 10.3934/dcds.2014.34.3383

[15]

Gernot Greschonig. Regularity of topological cocycles of a class of non-isometric minimal homeomorphisms. Discrete & Continuous Dynamical Systems - A, 2013, 33 (9) : 4305-4321. doi: 10.3934/dcds.2013.33.4305

[16]

Pavel Galashin, Vladimir Zolotov. Extensions of isometric embeddings of pseudo-Euclidean metric polyhedra. Electronic Research Announcements, 2016, 23: 1-7. doi: 10.3934/era.2016.23.001

[17]

E. Camouzis, H. Kollias, I. Leventides. Stable manifold market sequences. Journal of Dynamics & Games, 2018, 5 (2) : 165-185. doi: 10.3934/jdg.2018010

[18]

Camillo De Lellis, Emanuele Spadaro. Center manifold: A case study. Discrete & Continuous Dynamical Systems - A, 2011, 31 (4) : 1249-1272. doi: 10.3934/dcds.2011.31.1249

[19]

Zhiguo Feng, Ka-Fai Cedric Yiu. Manifold relaxations for integer programming. Journal of Industrial & Management Optimization, 2014, 10 (2) : 557-566. doi: 10.3934/jimo.2014.10.557

[20]

Sara Munday. On the derivative of the $\alpha$-Farey-Minkowski function. Discrete & Continuous Dynamical Systems - A, 2014, 34 (2) : 709-732. doi: 10.3934/dcds.2014.34.709

2018 Impact Factor: 1.143

Metrics

  • PDF downloads (8)
  • HTML views (0)
  • Cited by (1)

[Back to Top]