On the Willmore problem for surfaces with symmetries

讲座时间 Datetime: 2022年11月1日，星期二，14：30-16：00

地点 Venue: 腾讯线上会议：315 628 400

主持人 Host：吴志伟

报告人 Speaker: 王鹏 

单位 Affiliation: 福建师范大学

报告摘要 Abstract:

The famous Willmore conjectures states that the Clifford torus minimizes Willmore energy among all 2-tori in S^3, which was proved by Marques and Neves. For higher genus surfaces, it was conjectured by Kusner that the Lawson minimal surfaces \xi_{g,1} minimizes the Willmore energy for all immersions in S^3 with genus g>1. We show that it holds for surfaces in S^3 which have genus g>1 and are symmetric w. r. t. the group \tilde{G}_{g,1}. Here \tilde{G}_{g,1} denotes a group generated by halfturns about some great circles of S^3, which is a subgourp of the symmetric group of \xi_{g,1}. This is a joint work with Prof. Kusner (UMass Amherst) and Prof. Ying Lv (Xiamen Univ.).