On the Morse index and spectral properties of minimal submanifolds in spheres

报告专家：王鹏 （福建师范大学）

报告时间：2024年7月25日（星期四）下午15：10

报告地点：西南中心516

报告题目：On the Morse index and spectral properties of minimal submanifolds in spheres.

报告摘要：The Morse index and spectral properties of minimal

submanifolds in spheres connect several branches of geometry,analysis, topology and spectral theory. It is known that Urbano's estimate of index of minimal surfaces in 3-sphere plays an important role in Marques and Neves's proof of Willmore conjecture in the 3-sphere.In this talk we will recall several related topics on this direction and report our recent works on index estimate of minimal 2-tori, minimal hypersurfaces with \lamba_1<n and minimal products of minimal submanifolds.Classification of \lambda_1-minimal flat 3-tori and 4-tori will be also discussed briefly. These are based on joint works with Hang Chen, Rob Kusner, Ying Lv, Changping Wang and Zhenxiao Xie.

     专家简介：王鹏，福建师范大学数学与统计学院教授，闽江学者特聘教授，博士生导师；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3项，青年基金1项；在J. Diff. Geom., Adv. Math., J. Reine Angew 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。

邀请人：盛利