Speaker：Jiayu Li (University of Science and Technology of China)

Time：2024-12-30, 14:30

Location：Conference Room C503 at Administration Building at Haiyun Campus

Abstract:

Symplectic property is preserved along the mean curvature flow in Kähler-Einstein surface, which is called ”Symplectic mean curvature flow”. It was proved that there is no a Type I singularity for the symplectic mean curvature flow. In this paper, we will study the translating soliton which is an important model of a Type II singularity of the mean curvature flow. We first prove that a symplectic translating soliton must be a plane under some natural assumptions, we then demonstrate the necessity of these assumptions through an exploration of compelling examples. Furthermore, we find a necessary condition for the translating soliton being a blow-up limit of the symplectic mean curvature flow in a Kähler-Einstein surface. Finally, we use the necessary condition to exclude the translating soliton we construct as blow-up limits of the flow.This is a joint work with professor Han Xiaoli and professor Sun Jun.