no. 1
On the Geometry of Null Cones in Einstein-Vacuum Spacetimes
Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 1, pp. 285-328. 
@article{AIHPC_2009__26_1_285_0,
     author = {Wang, Qian},
     title = {On the {Geometry} of {Null} {Cones} in {Einstein-Vacuum} {Spacetimes}},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {285--328},
     publisher = {Elsevier},
     volume = {26},
     number = {1},
     year = {2009},
     doi = {10.1016/j.anihpc.2008.03.002},
     mrnumber = {2483823},
     zbl = {1157.83309},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2008.03.002/}
}
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Wang, Qian. On the Geometry of Null Cones in Einstein-Vacuum Spacetimes. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 1, pp. 285-328. doi : 10.1016/j.anihpc.2008.03.002. http://www.numdam.org/articles/10.1016/j.anihpc.2008.03.002/

[1] Choquet-Bruhat Y., Théorème D'existence Pour Certains Systemes D'équations Aux Dérivées Partielles Nonlinéaires, Acta Math. 88 (1952) 141-225. | MR | Zbl

[2] Christodoulou D., Klainerman S., The Global Nonlinear Stability of the Minkowski Space, Princeton Mathematical Series, vol. 41, Princeton, 1993. | MR | Zbl

[3] Hawking S. W., Ellis G. F.R., The Large Scale Structure of Space-Time, Cambridge Monographs on Mathematical Physics, 1973. | MR | Zbl

[4] Klainerman S., Francesco N., The Evolution Problem in General Relativity, Birkhäuser, 2003. | MR | Zbl

[5] Klainerman S., Machedon M., Space-Time Estimates for Null Forms and the Local Existence Theorem, Comm. Pure Appl. Math. 46 (1993) 1221-1268. | MR | Zbl

[6] S. Klainerman, I. Rodnianski, Unpublished notes, 2003.

[7] Klainerman S., Rodnianski I., Rough Solutions to the Einstein Vacuum Equations, Ann. of Math. 161 (2005) 1143-1193. | MR | Zbl

[8] Klainerman S., Rodnianski I., The Causal Structure of Microlocalized Rough Einstein Metrics, Ann. of Math. 161 (2005) 1195-1243. | MR | Zbl

[9] Klainerman S., Rodnianski I., Causal Geometry of Einstein-Vacuum Spacetimes With Finite Curvature Flux, Invent. Math. 159 (3) (2005) 437-529. | MR | Zbl

[10] Klainerman S., Rodnianski I., Bilinear Estimates on Curved Space-Times, J. Hyperbolic Differential Equations 2 (2005) 279-291. | MR

[11] Klainerman S., Rodnianski I., Sharp Trace Theorems for Null Hypersurfaces on Einstein Metrics With Finite Curvature Flux, Geom. Funct. Anal. 16 (1) (2006) 164-229. | MR

[12] Klainerman S., Rodnianski I., A Geometric Littlewood-Paley Theory, Geom. Funct. Anal. 16 (1) (2006) 126-163. | MR

[13] S. Klainerman, I. Rodnianski, On the radius of injectivity of null hypersurfaces, J. Amer. Math. Soc., to appear. | MR

[14] Klainerman S., Rodnianski I., A Kirchoff-Sobolev Parametrix for the Wave Equation and Applications, J. Hyperbolic Differential Equations 4 (3) (2007) 401-433. | MR | Zbl

[15] Klainerman S., Rodnianski I., On the Breakdown Criterion in General Relativity, http://arXiv:0801.1709.

[16] Poisson E., The Motion of Point Particles in Curved Spacetimes, www.livingreviews.org/lrr-2004-6. | Zbl

[17] Stein E. M., Topics in Harmonic Analysis Related to the Littlewood-Paley Theory, Annals of Mathematics Studies, vol. 63, Princeton University Press, 1970. | MR | Zbl

[18] Stein E. M., Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, With the assistance of Timothy S. Murphy, Princeton Mathematical Series, vol. 43, Princeton University Press, Princeton, NJ, 1993, Monographs in Harmonic Analysis III. | MR | Zbl

[19] Tao T., Harmonic Analysis in the Phase Plane, Lecture notes 254A, http://www.math.ucla.edu/~tao.

[20] Triebel H., Interpolation Theory, Function Spaces, Differential Operators, second ed., Johann Ambrosius Barth, Heidelberg, 1995. | MR | Zbl

[21] Wald R. M., General Relativity, University of Chicago Press, 1984. | MR | Zbl

[22] Q. Wang, Causal geometry of Einstein-vacuum spacetimes, Ph.D thesis of Princeton University, 2006. | MR

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