Plateau Stein Manifolds

2018/11/10 by Misha Gromov, Gromov, Misha · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG

paper · pdf · doi:10.48550/arxiv.1811.04316

arxiv created 2018/11/10 · openalex publication_date 2018/11/10 · arxiv updated 2018/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Geometric Convergence to an Extreme Limit Space with nonnegative scalar curvature

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