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arXiv · 2408.13864

An Alternative for Constant Mean Curvature Hypersurfaces

Liam Mazurowski·Xin Zhou
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Abstract

Let $M^{n+1}$ be a closed manifold of dimension $3\le n+1\le 7$ equipped with a generic Riemannian metric $g$. Let $c$ be a positive number. We show that, either there exist infinitely many distinct closed hypersurfaces with constant mean curvature equal to $c$, or there exist infinitely many distinct closed hypersurfaces with constant mean curvature less than $c$ but enclosing half the volume of $M$.

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Liam Mazurowski, Xin Zhou. 2024-08-25. An Alternative for Constant Mean Curvature Hypersurfaces. https://arxiv.org/abs/2408.13864

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