Mathematics – Analysis of PDEs
Scientific paper
2003-08-13
Mathematics
Analysis of PDEs
The previous version has been corrected for minor errors and exposition
Scientific paper
10.1007/s00222-004-0365-4
One of the central difficulties of settling the $L^2$-bounded curvature conjecture for the Einstein -Vacuum equations is to be able to control the causal structure of spacetimes with such limited regularity. In this paper we show how to circumvent this difficulty by showing that the geometry of null hypersurfaces of Enstein-Vacuum spacetimes can be controlled in terms of initial data and the total curvature flux through the hypersurface.
Klainerman Sergiu
Rodnianski Igor
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