Ricci curvature and minimal hypersurfaces with large Betti numbers
Differential Geometry
2026-04-01 v2 Geometric Topology
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.
Cite
@article{arxiv.2507.17305,
title = {Ricci curvature and minimal hypersurfaces with large Betti numbers},
author = {Davi Maximo and Philipp Reiser and Daniele Semola},
journal= {arXiv preprint arXiv:2507.17305},
year = {2026}
}
Comments
20 pages, minor changes in the main part, added appendix on deformations of invariant metrics of non-negative Ricci curvature, final version