We prove an interior estimate for the gradient function of space-like hypersurfaces which move by mean curvature in a Lorentzian manifold. This estimate depends only on a time fraction which measures how far the hypersurfaces are from being null. As a consequence, we show that under mean curvature flow a weakly spacelike initial hypersurface instantaneously becomes smooth and strictly spacelike except along null geodesics which extend to its boundary.
|Pages (from-to)||181 - 205|
|Number of pages||25|
|Journal||Communications in Analysis and Geometry|
|Publication status||Published - 2003|