Existence of minimal hypersurfaces in complete manifolds of finite volume
Abstract
We prove that every complete noncompact manifold of finite volume contains a (possibly noncompact) 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 $V + \varepsilon$.
 Publication:

arXiv eprints
 Pub Date:
 September 2016
 DOI:
 10.48550/arXiv.1609.04058
 arXiv:
 arXiv:1609.04058
 Bibcode:
 2016arXiv160904058C
 Keywords:

 Mathematics  Differential Geometry;
 49Q05;
 53A10
 EPrint:
 38 pages, 8 figures. Revised version