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arXiv · 2507.17305

Ricci curvature and minimal hypersurfaces with large Betti numbers

Davi Maximo·Philipp Reiser·Daniele Semola
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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.

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Davi Maximo, Philipp Reiser, Daniele Semola. 2025-07-23. Ricci curvature and minimal hypersurfaces with large Betti numbers. https://doi.org/10.1007/s00526-026-03283-8

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