Existence of minimal hypersurfaces in complete manifolds of finite volume
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Author(s)
Chambers, Gregory R
Liokumovich, Yevgeniy
Date Issued
August 2020
Journal
Inventiones mathematicae
Publisher
Springer Berlin Heidelberg
Citation
Chambers, Gregory R., and Yevgeniy Liokumovich, "Existence of minimal hypersurfaces in complete manifolds of finite volume." Inventiones mathematicae 219 (2020): 179-217 ©2020 Author(s)
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Author's final manuscript
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+ε.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s00222-019-00903-3
