王鹏教授学术报告：Morse Index & Willmore stability of minimal surfaces in S^n
发布时间：2022-10-01 浏览次数：115
报告人：王鹏教授（福建师范大学）
报告时间：2022年10月7日14:30-15:30
报告地点：育才校区数学楼304 腾讯会议（ID: 265-887-778）
报告题目：Morse Index & Willmore stability of minimal surfaces in S^n
报告摘要：The Willmore conjecture states that the Clifford torus minimizes uniquely the Willmore energy \int (H^2+1) dM among all tori in S^3, which is solved by Marques and Neves in 2012. An important basis of their proof is Urbano Theorem. In this talk we will show the following Urbano type theorem: for a minimal torus in S^4, its Morse Index >=6, with equality holding iff it is the Clifford torus.
For higher genus surfaces, it was conjectured by Kusner that the Lawson minimal surface, \xi_{m,1}: M-->S^3, minimizes uniquely among all genus m surfaces in S^n. In this talk, we will also show that this conjecture holds under the assumption that the (conformal) surfaces in S^n have the same conformal structure as \xi_{m,1}. This is based on joint works with Prof. Kusner.
报告人简介：王鹏，福建师范大学教授，闽江学者特聘教授，主要研究方向为Willmore曲面与极小曲面，主持国家自然科学基金面上项目2项，青年基金1项；在J. Diff. Geom., Adv. Math., Bull.London Math.Soc., Tohoku Math J., Pacific J.Math., Proc.AMS等期刊上发表学术论文20多篇。