Constructing Riemannian manifolds reveals embedded minimal hypersurfaces with specific Betti numbers, indicating significant geometric properties.
In any dimension n+1≥ 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.
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Maximo et al. (2026) studied this question.
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