Around the bounded $L^2$ curvature conjecture in general relativity

Klainerman, Sergiu; Rodnianski, Igor; Szeftel, Jeremie

doi:10.5802/jedp.53

Around the bounded

L^{2}

curvature conjecture in general relativity

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

Journées équations aux dérivées partielles (2008), article no. 9, 15 p.

Résumé

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

Affiliations des auteurs :

Klainerman, Sergiu ¹ ; Rodnianski, Igor ¹ ; Szeftel, Jeremie ²

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     title = {Around the bounded $L^2$ curvature conjecture in general relativity},
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     pages = {1--15},
     publisher = {Groupement de recherche 2434 du CNRS},
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     url = {http://archive.numdam.org/articles/10.5802/jedp.53/}
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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://archive.numdam.org/articles/10.5802/jedp.53/

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