Abstract and Applied Analysis

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

Ruiwei Xu and Linfen Cao

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 196751, 9 pages.

Dates
First available in Project Euclid: 6 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412607378

Digital Object Identifier
doi:10.1155/2014/196751

Mathematical Reviews number (MathSciNet)
MR3232825

Zentralblatt MATH identifier
07021914

Citation

Xu, Ruiwei; Cao, Linfen. Complete Self-Shrinking Solutions for Lagrangian Mean Curvature Flow in Pseudo-Euclidean Space. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 196751, 9 pages. doi:10.1155/2014/196751. https://projecteuclid.org/euclid.aaa/1412607378


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