Complete Self-Shrinking Solutions for Lagrangian Mean Curvature Flow in Pseudo-Euclidean Space
Joint Authors
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-07-06
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Xu, Ruiwei& Cao, Linfen. 2014. Complete Self-Shrinking Solutions for Lagrangian Mean Curvature Flow in Pseudo-Euclidean Space. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-9.
https://search.emarefa.net/detail/BIM-1013460
Modern Language Association (MLA)
Xu, Ruiwei& Cao, Linfen. Complete Self-Shrinking Solutions for Lagrangian Mean Curvature Flow in Pseudo-Euclidean Space. Abstract and Applied Analysis No. 2014 (2014), pp.1-9.
https://search.emarefa.net/detail/BIM-1013460
American Medical Association (AMA)
Xu, Ruiwei& Cao, Linfen. Complete Self-Shrinking Solutions for Lagrangian Mean Curvature Flow in Pseudo-Euclidean Space. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-9.
https://search.emarefa.net/detail/BIM-1013460
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1013460