We study time-like hypersurfaces with vanishing mean curvature in the (3+1) dimensional Minkowski space, which are the hyperbolic counterparts to minimal embeddings of Riemannian manifolds. The catenoid is a stationary solution of the associated Cauchy pro ...
We introduce a suitable concept of weak evolution in the context of the radial quintic focussing semilinear wave equation on R^{3+1}, that is adapted to continuation past type II singularities. We show that the weak extension leads to type I singularity fo ...
Under mild assumptions, we remove all traces of the axiom of choice from the construction of the maximal globally hyperbolic Cauchy development in general relativity. The construction relies on the notion of direct union manifolds, which we review. The con ...
We show that a stationary asymptotically flat electro-vacuum solution of Einstein's equations that is everywhere locally "almost isometric" to a Kerr-Newman solution cannot admit more than one event horizon. Axial symmetry is not assumed. In particular thi ...
