Global Nonlinear Stability of Minkowski Space for Spacelike-Characteristic Initial Data

In this paper the author proves the nonlinear global stability of Minkowski space in the framework of the spatial-characteristic Cauchy problem for the Einstein equations in vacuum. The spatial-characteristic initial data are prescribed on a 3-disk and on the future-complete zero hypersurface emanating from the boundary of this disk. The author's result extends the original result proved by Christodoulou and Klainerman for which the initial data are prescribed on a spatial hyperplane. The proof is based on the vector field method and the bootstrap argument introduced in Christodoulou-Klainerman. The main novelty is the introduction and control of new geometric constructions adapted to the characteristic-space framework. In particular, the author uses vertex-prescribed light cones, boundary-prescribed maximal spatial hypersurfaces, and global harmonic coordinates on Riemannian 3-disks.