Plateau-Stein manifolds

Mikhael Gromov

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)923-951
Number of pages29
JournalCentral European Journal of Mathematics
Volume12
Issue number7
DOIs
StatePublished - 2014

Fingerprint

Stein Manifold
Minimal Hypersurface
Morse Function
Positive Curvature
Mean Curvature
Finite Volume
Hypersurface
Riemannian Manifold

Keywords

  • Geometric measure theory
  • Riemannian manifolds
  • Stein Manifolds

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Plateau-Stein manifolds. / Gromov, Mikhael.

In: Central European Journal of Mathematics, Vol. 12, No. 7, 2014, p. 923-951.

Research output: Contribution to journalArticle

Gromov, Mikhael. / Plateau-Stein manifolds. In: Central European Journal of Mathematics. 2014 ; Vol. 12, No. 7. pp. 923-951.
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