Ricci curvature and minimal hypersurfaces with large Betti numbers
arXiv:2507.17305 · doi:10.1007/s00526-026-03283-8
Abstract
In any dimension we construct a sequence of closed -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.
20 pages, minor changes in the main part, added appendix on deformations of invariant metrics of non-negative Ricci curvature, final version