Entire Spacelike Hypersurfaces with Constant Curvature in Minkowski Space

We prove that, in the Minkowski space, if a spacelike, (n − 1)-convex hypersurface M with constant $\sigma_{n−1}$ curvature has bounded principal curvatures, then M is convex. Moreover, if M is not strictly convex, after an R^{n,1} rigid motion, M splits as a product $M^{n−1}\times R.$ We also construct nontrivial examples of strictly convex, spacelike hypersurfaces M with constant $\sigma_k$ curvature and bounded principal curvatures. This is a joint work with Changyu Ren and Zhizhang Wang.