Existence of minimal hypersurfaces in complete manifolds of finite volume
Author(s)Chambers, Gregory R; Liokumovich, Yevgeniy
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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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Springer Berlin Heidelberg
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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