On the symplectic mean curvature flows

：李嘉禹（中国科学技术大学）
：2024-12-30 14:30
：海韵园行政楼C503

报告人：李嘉禹（中国科学技术大学）

时  间：2024年12月30日14:30

地  点：海韵园行政楼C503

内容摘要:

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.

个人简介：

李嘉禹，中国科学技术大学杰出讲席教授、中法数学中心主任、国家基金委创新群体带头人、国家杰出青年科学基金获得者。研究领域为几何分析。曾任中国科学技术大学数学科学学院执行院长、中德几何分析伙伴小组组长、国际理论物理中心（ICTP） 研究员。学术刊物《中国科学》，《数学学报》等杂志编委，《JPDE》主编。曾任中国数学会常务理事、国家自然科学基金委员会“数学天元基金领导小组”成员。曾获得北京青年科技奖，香港求是基金会“杰出青年学者奖”，中国数学会“陈省身数学奖”，国家自然科学奖二等奖。

 

联系人：夏超