Multiple existence of minimal surfaces with low genus in lens spaces
报告人简介
王童瑞，现任上海交通大学长聘教轨副教授。2022年博士毕业于南京大学，2022-2024年于西湖大学任博士后工作。先后在北京大学北京国际数学研究中心和美国康奈尔大学交流访问。主要从事几何分析中极小曲面，常平均曲率曲面等几何变分问题的研究。相关研究成果发表于Adv.Math.,Math Ann.,Int.Math.Res.Not., Calc.Var.Partial Differ.Equ.等国际学术期刊。
内容简介
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.
