Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4604795 | Annales de l'Institut Henri Poincare (C) Non Linear Analysis | 2009 | 44 Pages |
Abstract
In this paper we study the geometry of null cones in smooth Einstein vacuum spacetimes. We provide the L∞ estimate for the trace of the null second fundamental form, as well as estimates for other geometric quantities. This paper is based on the work of Klainerman and Rodnianski [S. Klainerman, I. Rodnianski, Causal geometry of Einstein-vacuum spacetimes with finite curvature flux, Invent. Math. 159 (3) (2005) 437–529; S. Klainerman, I. Rodnianski, Sharp trace theorems for null hypersurfaces on Einstein metrics with finite curvature flux, Geom. Funct. Anal. 16 (1) (2006) 164–229; S. Klainerman, I. Rodnianski, A geometric Littlewood–Paley theory, Geom. Funct. Anal. 16 (1) (2006) 126–163].
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis