Preprint

Inserted: 24 jul 2025
Last Updated: 24 jul 2025

Year: 2025

Abstract:

In any dimension $n+1\ge 4$ we construct a sequence of closed $(n+1)$-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.

Keywords: Ricci curvature, Morse index, Minimal hypersurface

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• Minimal_hypersurfaces_and_positive_Ricci.pdf