We study the isometric spacelike embedding problem in scaled de Sitter space, and obtain Weyl-type estimates corresponding closedness space of embeddings.

We consider space-times which are asymptotically flat at spacelike infinity, i. It is well known that, in general, one cannot have a smooth differentiable structure at i, but have to use direction dependent structures. Instead of the oftenly used C-differentiabel structure, we suggest a weaker differential structure, a C + structure. The reason for this is that we have not seen any completions ...

A classification of 2-dimensional surfaces imbedded in spacetime is presented, according to the algebraic properties of their shape tensor. The classification has five levels, and provides among other things a refinement of the concepts of trapped, umbilical and extremal surfaces, which split into several different classes. The classification raises new important questions and opens many possib...

We prove the mean curvature flow of a spacelike graph in (Σ1 ×Σ2,g1 −g2) of a map f : Σ1 → Σ2 from a closed Riemannian manifold (Σ1,g1) with Ricci1 > 0 to a complete Riemannian manifold (Σ2,g2) with bounded curvature tensor and derivatives, and with K2 ≤ K1, remains a spacelike graph, exists for all time, and converges to a slice at infinity. We also show, with no need of the assumption K2 ≤ K1...