English

Plateau Stein Manifolds

Differential Geometry 2018-11-13 v1

Abstract

We study/construct (proper and non-proper) Morse functions on complete Riemannian manifolds, the level hypersurfaces of which have positive mean curvatures at all non-critical points. We show, for instance, that if a complete Rieannin manifold admits no such (not necessarily proper) function, then it contains a (possibly, singular) complete (possibly, compact) minimal hypersurface of finite volume.

Keywords

Cite

@article{arxiv.1811.04316,
  title  = {Plateau Stein Manifolds},
  author = {Misha Gromov},
  journal= {arXiv preprint arXiv:1811.04316},
  year   = {2018}
}
R2 v1 2026-06-23T05:11:35.550Z