Causal geometry of Einstein-vacuum spacetimes with finite curvature flux (Q1770269)

The authors investigate how to circumvent a difficulty in the \(L^2\)- bounded curvature conjecture by showing that the geometry of null hypersurfaces of the vacuum Einstein equations can be controlled by using the initial data and the total curvature flux through a null outgoing hypersurface: Contents include: Introduction; Null hypersurfaces; Motivation and second version of the Main Theorem; Bootstrap assumptions and preliminary estimates; Main estimates in Besov norms; Structure of error terms; Main estimates; and an Appendix on the fractional powers of the Laplace-Beltrami operator.