# Plateau-Stein manifolds

Open Mathematics (2014)

- Volume: 12, Issue: 7, page 923-951
- ISSN: 2391-5455

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topMisha Gromov. "Plateau-Stein manifolds." Open Mathematics 12.7 (2014): 923-951. <http://eudml.org/doc/269309>.

@article{MishaGromov2014,

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.},

author = {Misha Gromov},

journal = {Open Mathematics},

keywords = {Riemannian manifolds; Stein Manifolds; Geometric measure theory; Stein manifolds; geometric measure theory},

language = {eng},

number = {7},

pages = {923-951},

title = {Plateau-Stein manifolds},

url = {http://eudml.org/doc/269309},

volume = {12},

year = {2014},

}

TY - JOUR

AU - Misha Gromov

TI - Plateau-Stein manifolds

JO - Open Mathematics

PY - 2014

VL - 12

IS - 7

SP - 923

EP - 951

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.

LA - eng

KW - Riemannian manifolds; Stein Manifolds; Geometric measure theory; Stein manifolds; geometric measure theory

UR - http://eudml.org/doc/269309

ER -

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