Singularity of mean curvature flow of Lagrangian submanifolds

• 成果类型: Article
• 署名作者: Chen, JY; Li, JY
• 署名单位: University of British Columbia; Fudan University; Chinese Academy of Sciences
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-003-0332-5
• 发表日期: 2004
• 页码: 25-51
• 关键词: surfaces; inequalities; sobolev

摘要

In this article we study the tangent cones at first time singularity of a Lagrangian mean curvature flow. If the initial compact submanifold Sigma(0) is Lagrangian and almost calibrated by Re Ohm in a Calabi-Yau n-fold (M, Ohm), and T > 0 is the first blow-up time of the mean curvature flow, then the tangent cone of the mean curvature flow at a singular point (X-0, T) Is a stationary Lagrangian integer multiplicity current in R-2n with volume density greater than one at X-0. When n = 2, the tangent cone is a finite union of at least two 2-planes in R-4 which are complex in a complex structure on R-4.