Plateau-Stein manifolds

Misha Gromov

Type: Article

Publication Date: 2014-04-02

Citations: 24

DOI: https://doi.org/10.2478/s11533-013-0387-5

Abstract

Abstract We study/construct (proper and non-proper) Morse functions f on complete Riemannian manifolds X such that the hypersurfaces f(x) = t for all −∞ < t < +∞ have positive mean curvatures at all non-critical points x ∈ X of f. We show, for instance, that if X admits no such (not necessarily proper) function, then it contains a (possibly, singular) complete (possibly, compact) minimal hypersurface of finite volume.

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