Around the bounded L 2 curvature conjecture in general relativity
Sergiu Klainerman1 ; Igor Rodnianski1 ; Jeremie Szeftel2
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
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
Sergiu Klainerman 1 ; Igor Rodnianski 1 ; Jeremie Szeftel 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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Sergiu Klainerman; Igor Rodnianski; Jeremie Szeftel. 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. https://proceedings.centre-mersenne.org/articles/10.5802/jedp.53/

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