Problème de Cauchy spatial-caractéristique avec courbure L 2 en relativité générale

The present article is a summary of the papers [10] and [11] which establish a bounded L curvature theorem for the spacelike-characteristic Cauchy problem of general relativity. More precisely, we obtain a lower bound on the time of existence of classical solutions to the spacelikecharacteristic Cauchy problem for Einstein equations in vacuum, depending only on the L curvature fluxes through the initial spacelike and initial characteristic hypersurfaces and on suitable additional low regularity assumptions.