On the Willmore-minimizing problem for surfaces with symmetry 

组织者 Organizer:王鹏(福建师范大学,教授)
时间 Time: 2021年 9月7日15:00-16:00
地点 Venue:理科楼 (Science Building) A304

摘要 Abstract

It was conjectured by Prof. Rob Kusner in 1989 that the Lawson minimal surfaces \xi_{g,1} minimizes uniquely the Willmore energy among all genus-g, oriented, closed surfaces in S^n. When g=1, this reduces to the famous Willmore conjecture. In this talk we will introduce some process on this conjecture. We will first show that this conjecture holds if the surface in S^n has the same (induced) conformal structure as \xi_{g,1}. We will also show that this conjecture holds if the surface is contained in S^3 and is symmetric under the discrete group G_{g,1}. Here G_{g,1} is the group generated by some reflections which are used in Lawons's construction of \xi_{g,1}. Finally we will show that \xi_{g,1} is Willmore stable.

报告人简介 Profile

2002年本科毕业于兰州大学大学物理学专业,2008年获北京大学基础数学博士学位,2008年进入同济大学数学系工作,历任讲师,副教授,教授。2010-2011年间在德国慕尼黑工业大学数学系从事博士后研究,2016-2017年间在麻省大学阿莫斯特分校数学系访学。研究方向为微分几何。2018年8月进入福建师范大学数学与信息学院任教,主持国家自然科学基金面上项目1项、完成国家自然科学基金青年基金及数学天元各1项,在太平洋几何会议、微分几何与可积系统会议、中日几何会议、子流形的几何与拓扑等国际学术会议作邀请报告,在J. Diff. Geom、Adv math、Proc AMS、BLMS、Tohoku math J、Pacific math J等学术期刊上发表研究论文17篇,受邀论文2篇。