勷勤数学•专家报告

题      目：CMC hypersurfaces of finite index and Do Carmo's question in $\mathbb{R}^6$

报  告  人：洪寒 讲师  (邀请人：姚泽科)

                                             北京交通大学

时      间： 8月18日  15：00-16:00

地     点：数科院东楼401

报告人简介:

            洪寒，现为北京交通大学讲师。曾在清华大学丘成桐数学科学中心任职博士后。主要研究方向为微分几何与几何分析，研究兴趣为极小曲面等课题。相关研究成果发表在Crelle's journal, Adv. Math., CVPDE, JGA, IMRN等期刊上。

摘      要：

          In this talk, we will show that complete noncompact constant mean curvature hypersurfaces in $\mathbb{R}^6$ with finite index must be minimal. This result provides a positive answer to do Carmo's question in dimension $6$. The proof is also applicable to $\mathbb{R}^4$ and $\mathbb{R}^5$, thereby providing alternative proofs for those previously resolved cases. This is a joint work with Jingche chen and Haizhong Li.