The resolution of the bounded L 2 curvature conjecture in general relativity

Sergiu Klainerman[1]; Igor Rodnianski[1]; Jérémie Szeftel[2]

  • [1] Department of Mathematics Princeton University Princeton NJ 08544
  • [2] Laboratoire Jacques-Louis Lions Université Pierre et Marie Curie Paris 75005

Séminaire Laurent Schwartz — EDP et applications (2014-2015)

  • Volume: 202, Issue: 1, page 1-18
  • ISSN: 2266-0607

Abstract

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This paper reports on the recent proof of the bounded L 2 curvature conjecture. More precisely we show that the time of existence of a classical solution to the Einstein-vacuum equations depends only on the L 2 -norm of the curvature and a lower bound of the volume radius of the corresponding initial data set.

How to cite

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Klainerman, Sergiu, Rodnianski, Igor, and Szeftel, Jérémie. "The resolution of the bounded $L^2$ curvature conjecture in general relativity." Séminaire Laurent Schwartz — EDP et applications 202.1 (2014-2015): 1-18. <http://eudml.org/doc/275694>.

@article{Klainerman2014-2015,
abstract = {This paper reports on the recent proof of the bounded $L^2$ curvature conjecture. More precisely we show that the time of existence of a classical solution to the Einstein-vacuum equations depends only on the $L^2$-norm of the curvature and a lower bound of the volume radius of the corresponding initial data set.},
affiliation = {Department of Mathematics Princeton University Princeton NJ 08544; Department of Mathematics Princeton University Princeton NJ 08544; Laboratoire Jacques-Louis Lions Université Pierre et Marie Curie Paris 75005},
author = {Klainerman, Sergiu, Rodnianski, Igor, Szeftel, Jérémie},
journal = {Séminaire Laurent Schwartz — EDP et applications},
keywords = {Einstein vacuum equations; curvature bounds; causal geometry; quasilinear hyperbolic systems; radius of injectivity},
language = {eng},
number = {1},
pages = {1-18},
publisher = {Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {The resolution of the bounded $L^2$ curvature conjecture in general relativity},
url = {http://eudml.org/doc/275694},
volume = {202},
year = {2014-2015},
}

TY - JOUR
AU - Klainerman, Sergiu
AU - Rodnianski, Igor
AU - Szeftel, Jérémie
TI - The resolution of the bounded $L^2$ curvature conjecture in general relativity
JO - Séminaire Laurent Schwartz — EDP et applications
PY - 2014-2015
PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 202
IS - 1
SP - 1
EP - 18
AB - This paper reports on the recent proof of the bounded $L^2$ curvature conjecture. More precisely we show that the time of existence of a classical solution to the Einstein-vacuum equations depends only on the $L^2$-norm of the curvature and a lower bound of the volume radius of the corresponding initial data set.
LA - eng
KW - Einstein vacuum equations; curvature bounds; causal geometry; quasilinear hyperbolic systems; radius of injectivity
UR - http://eudml.org/doc/275694
ER -

References

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