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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.

séminaire laurent schwartz

Problème de Cauchy spatial-caractéristique avec courbure <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msup></mml:math> en relativité générale

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