  In this paper, we prove the global nonlinear stability of Minkowski space in
the context of the spacelike-characteristic Cauchy problem for Einstein vacuum
equations. Spacelike-characteristic initial data are posed on a compact 3-disk
and on the future complete null hypersurface emanating from its boundary. Our
result extends the seminal stability result for Minkowski space proved by
Christodoulou and Klainerman for which initial data are prescribed on a
spacelike 3-plane.
  The proof relies on the classical vectorfield method and bootstrapping
argument from Christodoulou-Klainerman. The main novelty is the introduction
and control of new geometric constructions adapted to the
spacelike-characteristic setting. In particular, it features null cones with
prescribed vertices, spacelike maximal hypersurfaces with prescribed boundaries
and global harmonic coordinates on Riemannian 3-disks.
