报告题目 (Title)： CMC hypersurface in hyperbolic space with finite index
中文标题：双曲空间中有限指标的常平均曲率曲面
报告人 (Speaker)：洪寒（北京交通大学）
报告时间 (Time)：2024年10月17日(周四) 1:30
报告地点 (Place)：校本部GJ403
邀请人(Inviter)：席东盟、李晋、吴加勇
报告摘要：Stable Bernstein problem asks whether two-sided stable minimal hypersurface must be hyperplane. Stability can be also defined on constant mean curvature (CMC) hypersurfaces. A similar question is asked by do Carmo on CMC hypersurfaces that whether stable ones must be “minimal” in general manifolds. In this talk, we will discuss some results about this question, especially in Euclidean space and hyperbolic space. In particular, we show that under certain assumption stable ones in hyperbolic space with mean curvature no less than one must have mean curvature one. The idea is the application of mu-bubble and harmonic function theory.