Ricci curvature and minimal hypersurfaces with large Betti numbers
Abstract
Abstract In any dimension $$n+1\ge 4$$ n + 1 ≥ 4 we construct a sequence of closed $$(n+1)$$ ( n + 1 ) -dimensional Riemannian manifolds with positive Ricci curvature admitting embedded two-sided minimal hypersurfaces such that the following hold: (i) any such hypersurface has Morse index one; (ii) the first Betti numbers of the hypsersurfaces are not uniformly bounded along the sequence.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Geometry and complex manifolds
Advanced Differential Geometry Research
Publication details
- Journal / source
- Calculus of Variations and Partial Differential Equations
- Volume
- 65
- Issue
- 4
- Publication date
- 7 March 2026
- Language
- EN