题目: Tangent flows of Lagrangian mean curvature flow (1)

报告人: 孙俊

日期: 2022年9月20日，15:00-17:00

腾讯会议：407-417-936

摘要：In this series of lectures, we will talk about the tangent flows of Lagrangian mean curvature flow in complex Euclidean spaces. More precisely, we will mainly talk about two aspects about the tangent flows of Lagrangian mean curvature flow:

(1)   Neves’ results on singularities of Lagrangian mean curvature flow for zero-Maslov class case, which states that the tangent flow of such a flow consists of a finite union of area-minimizing Lagrangian cones. Under the additional assumptions that the initial condition is an almost-calibrated and rational Lagrangian, connected components of the rescaled flow converges to a singlearea-minimizing Lagrangian cone;

(2)   Lotay-Schulze-Szekelyhidi’s recent result on neck pinches along the Lagrangian mean curvature flows of surfaces. They proved that for a zero-Maslov, rational Lagrangian mean curvature flow in a compact Calabi–Yau surface, if at the first singular time a tangent flow is given by the static union of two transverse planes, then the tangent flow is unique and the flow can be continued past the singularity as an immersed, smooth, zero-Maslov, rational Lagrangian mean curvature flow.

In this first lecture, we will collect the preliminaries on Lagrangian mean curvature flow and review Chen-Li’s result on singularities of Lagrangian mean curvature flow.

References:

   [1] J. Chen and J. Li, Singularity of mean curvature flow of Lagrangian submanifolds, Invent. Math. 156, 25-51, (2004).

   [2] A. Neves, Singularity of Lagrangian mean curvature flow, Invent. Math. 168, 449-484, (2007).

   [3] J. Lotay, F. Schulze and G. Szekelyhidi, Neck pinches along the Lagrangian mean curvature flow of surfaces, arXiv:2208.11054v1.