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 = {Sergiu Klainerman and Igor Rodnianski and J\'er\'emie Szeftel},
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},
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://slsedp.centre-mersenne.org/articles/10.5802/slsedp.65/}
}
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), Exposé no. 1, 18 p. doi : 10.5802/slsedp.65. https://slsedp.centre-mersenne.org/articles/10.5802/slsedp.65/
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