On the geometry of null cones in Einstein-vacuum spacetimes

Qian Wang

Annales de l'I.H.P. Analyse non linéaire (2009)

  • Volume: 26, Issue: 1, page 285-328
  • ISSN: 0294-1449

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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 26.1 (2009): 285-328. <http://eudml.org/doc/78841>.

@article{Wang2009,
author = {Wang, Qian},
journal = {Annales de l'I.H.P. Analyse non linéaire},
language = {eng},
number = {1},
pages = {285-328},
publisher = {Elsevier},
title = {On the geometry of null cones in Einstein-vacuum spacetimes},
url = {http://eudml.org/doc/78841},
volume = {26},
year = {2009},
}

TY - JOUR
AU - Wang, Qian
TI - On the geometry of null cones in Einstein-vacuum spacetimes
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2009
PB - Elsevier
VL - 26
IS - 1
SP - 285
EP - 328
LA - eng
UR - http://eudml.org/doc/78841
ER -

References

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  1. [1] Choquet-Bruhat Y., Théorème d'existence pour certains systemes d'équations aux dérivées partielles nonlinéaires, Acta Math.88 (1952) 141-225. Zbl0049.19201MR53338
  2. [2] Christodoulou D., Klainerman S., The Global Nonlinear Stability of the Minkowski Space, Princeton Mathematical Series, vol. 41, Princeton, 1993. Zbl0827.53055MR1316662
  3. [3] Hawking S.W., Ellis G.F.R., The Large Scale Structure of Space–Time, Cambridge Monographs on Mathematical Physics, 1973. Zbl0265.53054MR424186
  4. [4] Klainerman S., Francesco N., The Evolution Problem in General Relativity, Birkhäuser, 2003. Zbl1010.83004MR1946854
  5. [5] Klainerman S., Machedon M., Space–time estimates for null forms and the local existence theorem, Comm. Pure Appl. Math.46 (1993) 1221-1268. Zbl0803.35095MR1231427
  6. [6] S. Klainerman, I. Rodnianski, Unpublished notes, 2003. 
  7. [7] Klainerman S., Rodnianski I., Rough solutions to the Einstein vacuum equations, Ann. of Math.161 (2005) 1143-1193. Zbl1089.83006MR2180400
  8. [8] Klainerman S., Rodnianski I., The causal structure of microlocalized rough Einstein metrics, Ann. of Math.161 (2005) 1195-1243. Zbl1089.83007MR2180401
  9. [9] Klainerman S., Rodnianski I., Causal geometry of Einstein-vacuum spacetimes with finite curvature flux, Invent. Math.159 (3) (2005) 437-529. Zbl1136.58018MR2125732
  10. [10] Klainerman S., Rodnianski I., Bilinear estimates on curved space–times, J. Hyperbolic Differential Equations2 (2005) 279-291. Zbl1284.58018MR2151111
  11. [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. Zbl1206.35081MR2221255
  12. [12] Klainerman S., Rodnianski I., A geometric Littlewood–Paley theory, Geom. Funct. Anal.16 (1) (2006) 126-163. Zbl1206.35080MR2221254
  13. [13] S. Klainerman, I. Rodnianski, On the radius of injectivity of null hypersurfaces, J. Amer. Math. Soc., to appear. Zbl1198.53057MR2393426
  14. [14] Klainerman S., Rodnianski I., A Kirchoff–Sobolev parametrix for the wave equation and applications, J. Hyperbolic Differential Equations4 (3) (2007) 401-433. Zbl1148.35042MR2339803
  15. [15] Klainerman S., Rodnianski I., On the breakdown criterion in general relativity, http://arXiv:0801.1709. Zbl1203.35084
  16. [16] Poisson E., The motion of point particles in curved spacetimes, www.livingreviews.org/lrr-2004-6. Zbl1071.83011
  17. [17] Stein E.M., Topics in Harmonic Analysis Related to the Littlewood–Paley Theory, Annals of Mathematics Studies, vol. 63, Princeton University Press, 1970. Zbl0193.10502MR252961
  18. [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. Zbl0821.42001MR1232192
  19. [19] Tao T., Harmonic analysis in the phase plane, Lecture notes 254A, http://www.math.ucla.edu/~tao. 
  20. [20] Triebel H., Interpolation Theory, Function Spaces, Differential Operators, second ed., Johann Ambrosius Barth, Heidelberg, 1995. Zbl0830.46028MR1328645
  21. [21] Wald R.M., General Relativity, University of Chicago Press, 1984. Zbl0549.53001MR757180
  22. [22] Q. Wang, Causal geometry of Einstein-vacuum spacetimes, Ph.D thesis of Princeton University, 2006. MR2624235

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