BIMSA >
Differential Geometry Seminar
CMC hypersurfaces of finite index and Do Carmo's question in $\mathbb{R}^6$
CMC hypersurfaces of finite index and Do Carmo's question in $\mathbb{R}^6$
Organizers
Speaker
Han Hong
Time
Tuesday, June 3, 2025 2:45 PM - 4:30 PM
Venue
A3-4-301
Online
Zoom 815 762 8413
(BIMSA)
Abstract
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.