This paper reports on the recent proof of the bounded curvature conjecture. More precisely we show that the time of existence of a classical solution to the Einstein-vacuum equations depends only on the -norm of the curvature and a lower bound of the volume radius of the corresponding initial data set.
@article{SLSEDP_2014-2015____A1_0,
author = {Klainerman, Sergiu and Rodnianski, Igor and Szeftel, J\'er\'emie},
title = {The resolution of the bounded $L^2$ curvature conjecture in general relativity},
journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications},
note = {talk:1},
pages = {1--18},
publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
year = {2014-2015},
doi = {10.5802/slsedp.65},
language = {en},
url = {https://www.numdam.org/articles/10.5802/slsedp.65/}
}
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 N1 - talk:1 PY - 2014-2015 SP - 1 EP - 18 PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique UR - https://www.numdam.org/articles/10.5802/slsedp.65/ DO - 10.5802/slsedp.65 LA - en ID - SLSEDP_2014-2015____A1_0 ER -
%0 Journal Article %A Klainerman, Sergiu %A Rodnianski, Igor %A Szeftel, Jérémie %T The resolution of the bounded $L^2$ curvature conjecture in general relativity %J Séminaire Laurent Schwartz — EDP et applications %Z talk:1 %D 2014-2015 %P 1-18 %I Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique %U https://www.numdam.org/articles/10.5802/slsedp.65/ %R 10.5802/slsedp.65 %G en %F SLSEDP_2014-2015____A1_0
Klainerman, Sergiu; Rodnianski, Igor; Szeftel, Jérémie. The resolution of the bounded $L^2$ curvature conjecture in general relativity. Séminaire Laurent Schwartz — EDP et applications (2014-2015), Talk no. 1, 18 p. doi : 10.5802/slsedp.65. https://www.numdam.org/articles/10.5802/slsedp.65/
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