Hyperbolic mean curvature flow in Minkowski space

We study the hyperbolic mean curvature flow (HMCF) of graphs in Minkowski space. A quasilinear wave equation is derived and studied for the motion of smooth immersed spacelike acausal closed curves under HMCF. Based on this, we investigate the formation of singularities in the motion of these curves. Some blow-up results have been obtained and the estimates on the life-span of the solutions are given. Furthermore, our results show that the curvature of the limit curve become unbounded as t→Tmax.