Multiple existence of minimal surfaces with low genus in lens spaces
報告人簡介
王童瑞，現任上海交通大學長聘教軌副教授。2022年博士畢業于南京大學，2022-2024年于西湖大學任博士后工作。先后在北京大學北京國際數學研究中心和美國康奈爾大學交流訪問。主要從事幾何分析中極小曲面，常平均曲率曲面等幾何變分問題的研究。相關研究成果發表于Adv.Math.,Math Ann.,Int.Math.Res.Not., Calc.Var.Partial Differ.Equ.等國際學術期刊。
內容簡介
In this talk, I will discuss two either-or results for the multiple existences of minimal real projective planes and minimal Klein bottles in certain lens spaces with generic metrics. In particular, we show in positive Ricci RP^3 that there are four distinct minimal real projective planes together with four distinct minimal tori, and the number of minimal tori can be improved to five for almost all metrics of positive Ricci. Our proof is mainly based on a variant multiplicity one theorem for the Simon-Smith min-max theory under certain equivariant settings. This talk is based on the joint work with Xingzhe Li and Xuan Yao.
