Existence of minimal hypersurfaces in complete manifolds of finite volume

Author(s)
Chambers, Gregory R; Liokumovich, Yevgeniy
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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+ε.
Date issued
2020-08
URI
https://hdl.handle.net/1721.1/128678
Department
Massachusetts Institute of Technology. Department of Mathematics
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)
Version: Author's final manuscript
ISSN
0020-9910
1432-1297
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