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2014 Complete Self-Shrinking Solutions for Lagrangian Mean Curvature Flow in Pseudo-Euclidean Space
Ruiwei Xu, Linfen Cao
Abstr. Appl. Anal. 2014(SI41): 1-9 (2014). DOI: 10.1155/2014/196751

Abstract

Let f ( x ) be a smooth strictly convex solution of det ( 2 f / x i x j ) = exp ( 1 / 2 ) i = 1 n x i ( f / x i ) - f defined on a domain Ω R n ; then the graph M f of f is a space-like self-shrinker of mean curvature flow in Pseudo-Euclidean space R n 2 n with the indefinite metric d x i d y i . In this paper, we prove a Bernstein theorem for complete self-shrinkers. As a corollary, we obtain if the Lagrangian graph M f is complete in R n 2 n and passes through the origin then it is flat.

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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

Information

Published: 2014
First available in Project Euclid: 6 October 2014

zbMATH: 07021914
MathSciNet: MR3232825
Digital Object Identifier: 10.1155/2014/196751

Rights: Copyright © 2014 Hindawi

Vol.2014 • No. SI41 • 2014
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