# American Institute of Mathematical Sciences

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 findingisometric immersions into the Minkowski spacetime for hypersurfaces of a Lorentzian manifold.Our approach encompasses metrics having Sobolev regularity and Riemann curvature definedin the distributional sense, only.It applies to timelike, spacelike, or null hypersurfaces with arbitrary signature that possibly changesfrom 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, 2009, 23 (1&2) : 341-365. doi: 10.3934/dcds.2009.23.341
 [1] Marian Gidea, Rafael de la Llave, Tere M. Seara. A general mechanism of instability in Hamiltonian systems: Skipping along a normally hyperbolic invariant manifold. Discrete & Continuous Dynamical Systems, 2020, 40 (12) : 6795-6813. doi: 10.3934/dcds.2020166 [2] M. Phani Sudheer, Ravi S. Nanjundiah, A. S. Vasudeva Murthy. Revisiting the slow manifold of the Lorenz-Krishnamurthy quintet. Discrete & Continuous Dynamical Systems - B, 2006, 6 (6) : 1403-1416. doi: 10.3934/dcdsb.2006.6.1403 [3] Sara Munday. On the derivative of the $\alpha$-Farey-Minkowski function. Discrete & Continuous Dynamical Systems, 2014, 34 (2) : 709-732. doi: 10.3934/dcds.2014.34.709 [4] Dingheng Pi. Periodic orbits for double regularization of piecewise smooth systems with a switching manifold of codimension two. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021080 [5] Qiao Liu. Partial regularity and the Minkowski dimension of singular points for suitable weak solutions to the 3D simplified Ericksen–Leslie system. Discrete & Continuous Dynamical Systems, 2021  doi: 10.3934/dcds.2021041 [6] Yuxin Tan, Yijing Sun. The Orlicz Minkowski problem involving $0 < p < 1$: From one constant to an infinite interval. Discrete & Continuous Dynamical Systems - S, 2021  doi: 10.3934/dcdss.2021037 [7] Feng-Bin Wang, Xueying Wang. A general multipatch cholera model in periodic environments. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021105 [8] John Villavert. On problems with weighted elliptic operator and general growth nonlinearities. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021023 [9] Bernard Bonnard, Jérémy Rouot. Geometric optimal techniques to control the muscular force response to functional electrical stimulation using a non-isometric force-fatigue model. Journal of Geometric Mechanics, 2021, 13 (1) : 1-23. doi: 10.3934/jgm.2020032 [10] Xianming Liu, Guangyue Han. A Wong-Zakai approximation of stochastic differential equations driven by a general semimartingale. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2499-2508. doi: 10.3934/dcdsb.2020192 [11] Yu Yang, Jinling Zhou, Cheng-Hsiung Hsu. Critical traveling wave solutions for a vaccination model with general incidence. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021087 [12] Nouressadat Touafek, Durhasan Turgut Tollu, Youssouf Akrour. On a general homogeneous three-dimensional system of difference equations. Electronic Research Archive, , () : -. doi: 10.3934/era.2021017 [13] Yulia O. Belyaeva, Björn Gebhard, Alexander L. Skubachevskii. A general way to confined stationary Vlasov-Poisson plasma configurations. Kinetic & Related Models, 2021, 14 (2) : 257-282. doi: 10.3934/krm.2021004 [14] Hui Yang, Yuzhu Han. Initial boundary value problem for a strongly damped wave equation with a general nonlinearity. Evolution Equations & Control Theory, 2021  doi: 10.3934/eect.2021019 [15] Manfred Einsiedler, Elon Lindenstrauss. On measures invariant under diagonalizable actions: the Rank-One case and the general Low-Entropy method. Journal of Modern Dynamics, 2008, 2 (1) : 83-128. doi: 10.3934/jmd.2008.2.83 [16] A. Aghajani, S. F. Mottaghi. Regularity of extremal solutions of semilinaer fourth-order elliptic problems with general nonlinearities. Communications on Pure & Applied Analysis, 2018, 17 (3) : 887-898. doi: 10.3934/cpaa.2018044 [17] Yaonan Ma, Li-Zhi Liao. The Glowinski–Le Tallec splitting method revisited: A general convergence and convergence rate analysis. Journal of Industrial & Management Optimization, 2021, 17 (4) : 1681-1711. doi: 10.3934/jimo.2020040 [18] Wenjuan Zhao, Shunfu Jin, Wuyi Yue. A stochastic model and social optimization of a blockchain system based on a general limited batch service queue. Journal of Industrial & Management Optimization, 2021, 17 (4) : 1845-1861. doi: 10.3934/jimo.2020049 [19] Wenyuan Wang, Ran Xu. General drawdown based dividend control with fixed transaction costs for spectrally negative Lévy risk processes. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020179 [20] Zhikun She, Xin Jiang. Threshold dynamics of a general delayed within-host viral infection model with humoral immunity and two modes of virus transmission. Discrete & Continuous Dynamical Systems - B, 2021, 26 (7) : 3835-3861. doi: 10.3934/dcdsb.2020259

2019 Impact Factor: 1.338