Finite index constant mean curvature hypersurfaces in low dimensions

YMSC-BJTU Geometry seminar

Organizer：

Han Hong, Zhifei Zhu

Speaker：

Ivan Miranda de Almeida (IMPA)

Time：

9-10 am (Beijing Time)

June 3rd, 2026

Online：

Zoom Meeting ID: 891 8508 1544

Passcode: YMSC123

Title：

Finite index constant mean curvature hypersurfaces in low dimensions

Abstract:

We prove that every complete finite index immersed CMC hypersurface is either minimal or compact, provided that the ambient six-dimensional manifold is a Riemannian product of a closed manifold with non-negative sectional curvature and a Euclidean factor. As a consequence, we complete the classification of two-sided, complete weakly stable CMC hypersurfaces immersed in the space forms of positive curvature in dimension six. We also prove that every complete finite index CMC hypersurface immersed in the hyperbolic six-space with $|H|>7$ is compact. These results are closely related to questions posed by M. P. do Carmo, O. Chodosh and H. Hong.

Introduction: Ivan Miranda de Almeida is currently a Ph.D. student at IMPA under the supervision of Prof. Lucas Ambrozio. His research focuses on Geometric Analysis, particularly on the theory of constant mean curvature hypersurfaces.