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

Ruiwei Xu and Linfen Cao

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

Abstract: Let f(x) be a smooth strictly convex solution of det(∂2f/∂xi∂xj)=exp(12/)∑i=1nxi(∂f/∂xi)-f defined on a domain Ω⊂Rn; then the graph M∇f of ∇f is a space‐like self‐shrinker of mean curvature flow in Pseudo‐Euclidean space Rn2n with the indefinite metric ∑dxidyi. 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 Rn2n and passes through the origin then it is flat.

Date: 2014
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2014/196751

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:196751

Access Statistics for this article

More articles in Abstract and Applied Analysis from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().