Closed minimal surfaces of index one in Riemannian manifolds

Fernando C. Marques; André Neves

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arXiv · 2606.03583

Closed minimal surfaces of index one in Riemannian manifolds

Fernando C. Marques·André Neves

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Abstract

In this paper we prove that an $(n+1)$-manifold, compactly $n$-enlargeable, where $3\leq (n+1)\leq 7$, has connected, immersed Morse index one, closed minimal hypersurfaces with unbounded volumes for bumpy metrics. We prove that in the three-dimensional case the hypersurfaces are geometrically distinct using cyclic coverings of manifolds with boundary. The proof extends to $(n+1)$-fiberings. We prove a scalar curvature rigidity theorem for area-nonincreasing maps of three-dimensional manifolds. The case of stable surfaces is also discussed by using cohomology classes and incompressible surfaces.

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BibTeX RIS

Fernando C. Marques, André Neves. 2026-06-02. Closed minimal surfaces of index one in Riemannian manifolds. https://arxiv.org/abs/2606.03583

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