Complete Self-Shrinking Solutions for Lagrangian Mean Curvature Flow in Pseudo-Euclidean Space
Let f(x) be a smooth strictly convex solution of det(∂2f/∂xi∂xj)=exp(1/2)∑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 th...
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/196751 |
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| author | Ruiwei Xu Linfen Cao |
| author_facet | Ruiwei Xu Linfen Cao |
| author_sort | Ruiwei Xu |
| collection | DOAJ |
| description | Let f(x) be a smooth strictly convex solution of det(∂2f/∂xi∂xj)=exp(1/2)∑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. |
| format | Article |
| id | doaj-art-ab64741bdffa4bdc8b77b37a0c9a5099 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-ab64741bdffa4bdc8b77b37a0c9a50992025-02-03T01:22:28ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/196751196751Complete Self-Shrinking Solutions for Lagrangian Mean Curvature Flow in Pseudo-Euclidean SpaceRuiwei Xu0Linfen Cao1Department of Mathematics, Henan Normal University, Xinxiang, Henan 453007, ChinaDepartment of Mathematics, Henan Normal University, Xinxiang, Henan 453007, ChinaLet f(x) be a smooth strictly convex solution of det(∂2f/∂xi∂xj)=exp(1/2)∑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.http://dx.doi.org/10.1155/2014/196751 |
| spellingShingle | Ruiwei Xu Linfen Cao Complete Self-Shrinking Solutions for Lagrangian Mean Curvature Flow in Pseudo-Euclidean Space Abstract and Applied Analysis |
| title | Complete Self-Shrinking Solutions for Lagrangian Mean Curvature Flow in Pseudo-Euclidean Space |
| title_full | Complete Self-Shrinking Solutions for Lagrangian Mean Curvature Flow in Pseudo-Euclidean Space |
| title_fullStr | Complete Self-Shrinking Solutions for Lagrangian Mean Curvature Flow in Pseudo-Euclidean Space |
| title_full_unstemmed | Complete Self-Shrinking Solutions for Lagrangian Mean Curvature Flow in Pseudo-Euclidean Space |
| title_short | Complete Self-Shrinking Solutions for Lagrangian Mean Curvature Flow in Pseudo-Euclidean Space |
| title_sort | complete self shrinking solutions for lagrangian mean curvature flow in pseudo euclidean space |
| url | http://dx.doi.org/10.1155/2014/196751 |
| work_keys_str_mv | AT ruiweixu completeselfshrinkingsolutionsforlagrangianmeancurvatureflowinpseudoeuclideanspace AT linfencao completeselfshrinkingsolutionsforlagrangianmeancurvatureflowinpseudoeuclideanspace |