Complete Self-Shrinking Solutions for Lagrangian Mean Curvature Flow in Pseudo-Euclidean Space

Let ( ) be a smooth strictly convex solution of det( 2 / ) = exp {(1/2) ∑ =1 ( / ) − } defined on a domain Ω ⊂ R ; then the graph ∇ of ∇ is a space-like self-shrinker of mean curvature flow in Pseudo-Euclidean space R 2 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 2 and passes through the origin then it is flat