Singularity of mean curvature flow of Lagrangian submanifolds

By Jingyi Chen, Jiayu Li. 2003

78 citations recorded by the source corpus.

In this article we study the tangent cones at first time singularity of a Lagrangian mean curvature flow. If the initial compact submanifold Σ0 is Lagrangian and almost calibrated by ReΩ in a Calabi-Yau n-fold (M,Ω), 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 (X0,T) is a stationary Lagrangian integer multiplicity current in R2n with volume density greater than one at X0. When n=2, the tangent cone is a finite union of at least two 2-planes in R4 which are complex in a complex structure on R4.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/981b5ce527f10cd35a816f6b61d785387e2a8f38

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In Applied Mathematics

1. Knut Smoczyk
2. D. Joyce
3. Y. Xin
4. Qi Ding

In Geometry and Topology

1. Knut Smoczyk
2. D. Joyce
3. Y. Xin
4. Qi Ding

Citations in the corpus

• Self-similar solutions and translating solitons for Lagrangian mean curvature flow (2008, unknown): “The first one is due to Wang [26], and Chen and Li [6] independently, who observed that mean curvature flow for almost calibrated Lagrangians in Calabi–Yau n-folds cannot develop type I singularities.”
• Mean Curvature Flow in Higher Codimension: Introduction and Survey (2011, background): “of the results of Wang, Chen and Li in [17, 86] w.”