报告名称：Rigidity of self-shrinkers and related problems

主办单位：数学与统计学学院

报告专家：邱红兵副教授

专家所在单位：武汉大学

报告时间：2019年12月13日下午16：00-17：00

报告地点：数学与统计学学院201报告厅

专家简介：邱红兵，武汉大学，博士，副教授，研究生导师。发表SCI论文10多篇，部分工作发表在《Advances in Mathematics》等国际重要学术期刊上，主持国家自然科学基金青年、面上各一项。

报告摘要：In this talk, we shall introduce our recent work on self-shrinkers and its related topics. Firstly, we study the mean curvature flow of hyper-Lagrangian manifolds L^{2n} in hyper-kaehler manifolds M^{4n}. When n>1, we proved that such hyper-Lagrangian manifolds must be complex Lagrangian. So we only need to consider the case n=1, by the observation that any surface in 4-dim hyper-Kaehler manifolds is hyper-Lagrangian automatically and the complex phase map of self-shrinking surfaces is a generalized harmonic map, we showed that any complete proper self-shrinking surfaces in R^4 with the image of the complex phase map contained in S^2 omit the closed half of the great circle must be plane. Based on this rigidity and the blow up technique of mean curvature flow, we conclude that the corresponding MCF from closed surfaces with the image of the complex phase map contained in S^2 omit the closed half of the great circle does not de

邀请人：毛井