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arXiv · 1609.04058

Existence of minimal hypersurfaces in complete manifolds of finite volume

Gregory R. Chambers·Yevgeny Liokumovich
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Abstract

We prove that every complete non-compact manifold of finite volume contains a (possibly non-compact) minimal hypersurface of finite volume. The main tool is the following result of independent interest: if a region $U$ can be swept out by a family of hypersurfaces of volume at most $V$, then it can be swept out by a family of mutually disjoint hypersurfaces of volume at most $V + \varepsilon$.

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Gregory R. Chambers, Yevgeny Liokumovich. 2016-09-13. Existence of minimal hypersurfaces in complete manifolds of finite volume. https://arxiv.org/abs/1609.04058

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