Singularity of mean curvature flow of Lagrangian submanifolds
Singularity of mean curvature flow of Lagrangian submanifolds
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DOI：
10.1007/s00222-003-0332-5
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发表时间：
2003-01
影响因子：
3.1
通讯作者：
Jingyi Chen;Jiayu Li
中科院分区：
文献类型：
--
作者：
Jingyi Chen;Jiayu Li
本文研究了拉格朗日平均曲率流的切锥第一次奇异性。若初始紧致子流形X 0是Lagrange子流形，且几乎用ReΩ标定，且T>0是平均曲率流的第一次爆破时刻，则平均曲率流在奇点（X 0，T）处的切锥是R2 n中的定常Lagrange整数重流，且在X 0处的体积密度大于1.当n =2时，切锥是R4中至少两个2-平面的有限并，它们在R4上是复结构。
In this article we study the tangent cones at first time singularity of a Lagrangian mean curvature flow. If the initial compact submanifold Σ0is Lagrangian and almost calibrated by ReΩ in a Calabi-Yaun-fold (M,Ω), andT>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 (X0,T) is a stationary Lagrangian integer multiplicity current inR2nwith volume density greater than one atX0. Whenn=2, the tangent cone is a finite union of at least two 2-planes inR4which are complex in a complex structure onR4.