Time: 2019-06-10 10：00-11：00

Venue: Room 201 Lecture Hall

Abstract:

In this talk, we firstly prove that every hyper-Lagrangian submanifold L^{2n}(n > 1) in a hyperkaehler 4n-manifold is a complex Lagrangian submanifold. Secondly, we study the geometry of hyper-Lagrangian surfaces and demonstrate an optimal rigidity theorem with the condition on the complex phase map of self-shrinking surfaces in R^4 . Last but not least, we show that the mean curvature flow from a closed surface with the image of the complex phase map contained in S^2\(S^1_{+}) in a hyperkaehler 4-manifold does not develop any Type I singularity. This is a joint work with Dr. Linlin Sun.