Existence of minimal hypersurfaces in complete manifolds of finite\n volume

2016/09/13 by Gregory R. Chambers, Chambers, Gregory R., Yevgeny Liokumovich +1 · 1 citation
Mathematics · #49Q05 #53A10 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1609.04058

openalex publication_date 2016/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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• Mountain Pass Critical Points of the Volume Constrained Area Functional

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