Existence of minimal hypersurfaces in complete manifolds of finite volume

Existence of minimal hypersurfaces in complete manifolds of finite volume

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 s...

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Bibliographic Details
Main Authors: Chambers, Gregory R (Author), Liokumovich, Yevgeniy (Author)
Other Authors: Massachusetts Institute of Technology. Department of Mathematics (Contributor)
Format: Article
Language:English
Published: Springer Berlin Heidelberg, 2020-11-30T15:58:14Z.
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Online Access:Get fulltext
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100 1 0 |a Chambers, Gregory R  |e author 
100 1 0 |a Massachusetts Institute of Technology. Department of Mathematics  |e contributor 
700 1 0 |a Liokumovich, Yevgeniy  |e author 
245 0 0 |a Existence of minimal hypersurfaces in complete manifolds of finite volume 
260 |b Springer Berlin Heidelberg,   |c 2020-11-30T15:58:14Z. 
856 |z Get fulltext  |u https://hdl.handle.net/1721.1/128678 
520 |a 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. 
546 |a en 
655 7 |a Article 
773 |t 10.1007/s00222-019-00903-3 
773 |t Inventiones mathematicae 

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