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Abstract and Applied Analysis
Volume 2014, Article ID 196751, 9 pages
http://dx.doi.org/10.1155/2014/196751
Research Article

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

Department of Mathematics, Henan Normal University, Xinxiang, Henan 453007, China

Received 14 January 2014; Accepted 15 June 2014; Published 6 July 2014

Academic Editor: Ljubomir B. Ćirić

Copyright © 2014 Ruiwei Xu and Linfen Cao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.