Remarks on minimal hypersurfaces in shrinking gradient Ricci solitons
Abstract
In this paper, we prove that any compact 2-sided smooth stable minimal hypersurface in a shrinking gradient Ricci soliton $(M^{n},g,f)$ with scalar curvature $R\geq(n-1)\lambda$ must have vanished second fundamental form and vanished normal Ricci curvature. For shrinking gradient Ricci solitons with scalar curvature $R\geq(n-1)\lambda$, the existence of an area-minimizing hypersurface would imply that $M$ is splitting.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Nonlinear Partial Differential Equations
Advanced Differential Geometry Research
Publication details
- Journal / source
- Communications in Analysis and Geometry
- Volume
- 34
- Issue
- 1
- Pages
- 27–38
- Publication date
- 1 January 2026
- Language
- EN