Plateau-Stein manifolds

Misha Gromov

doi:10.2478/s11533-013-0387-5

Plateau-Stein manifolds

Misha Gromov

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	923-951
Number of pages	29
Journal	Central European Journal of Mathematics
Volume	12
Issue number	7
DOIs	https://doi.org/10.2478/s11533-013-0387-5
State	Published - Jul 2014

Keywords

Geometric measure theory
Riemannian manifolds
Stein Manifolds

ASJC Scopus subject areas

General Mathematics

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10.2478/s11533-013-0387-5

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AB - 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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KW - Riemannian manifolds

KW - Stein Manifolds

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Plateau-Stein manifolds

Abstract

Keywords

ASJC Scopus subject areas

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