Let be a smooth strictly convex solution of defined on a domain ; then the graph of is a space-like self-shrinker of mean curvature flow in Pseudo-Euclidean space with the indefinite metric . In this paper, we prove a Bernstein theorem for complete self-shrinkers. As a corollary, we obtain if the Lagrangian graph is complete in and passes through the origin then it is flat.
Ruiwei Xu. Linfen Cao. "Complete Self-Shrinking Solutions for Lagrangian Mean Curvature Flow in Pseudo-Euclidean Space." Abstr. Appl. Anal. 2014 (SI41) 1 - 9, 2014. https://doi.org/10.1155/2014/196751