Around the bounded L 2 curvature conjecture in general relativity
Journées équations aux dérivées partielles (2008), article no. 9, 15 p.

We report on recent progress obtained on the construction and control of a parametrix to the homogeneous wave equation g φ=0, where is a rough metric satisfying the Einstein vacuum equations. Controlling such a parametrix as well as its error term when one only assumes L 2 bounds on the curvature tensor R of is a major step towards the proof of the bounded L 2 curvature conjecture.

DOI : 10.5802/jedp.53
Klainerman, Sergiu 1 ; Rodnianski, Igor 1 ; Szeftel, Jeremie 2

1 Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton NJ 08544-1000 USA
2 Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton NJ 08544-1000 USA and Mathématiques Appliquées de Bordeaux, UMR CNRS 5466, Université Bordeaux 1, 351 cours de la Libération, 33405 Talence cedex FRANCE
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Klainerman, Sergiu; Rodnianski, Igor; Szeftel, Jeremie. Around the bounded $L^2$ curvature conjecture in general relativity. Journées équations aux dérivées partielles (2008), article  no. 9, 15 p. doi : 10.5802/jedp.53. http://www.numdam.org/articles/10.5802/jedp.53/

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