Plateau-Stein manifolds
Misha Gromov
Open Mathematics, Tome 12 (2014), p. 923-951 / Harvested from The Polish Digital Mathematics Library

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.

Publié le : 2014-01-01
EUDML-ID : urn:eudml:doc:269309
@article{bwmeta1.element.doi-10_2478_s11533-013-0387-5,
     author = {Misha Gromov},
     title = {Plateau-Stein manifolds},
     journal = {Open Mathematics},
     volume = {12},
     year = {2014},
     pages = {923-951},
     zbl = {1293.31006},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0387-5}
}
Misha Gromov. Plateau-Stein manifolds. Open Mathematics, Tome 12 (2014) pp. 923-951. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0387-5/

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