Contracting convex hypersurfaces in Riemannian manifolds by their mean curvature. (English) Zbl 0589.53058

The author generalizes results he obtained earlier [cf. J. Differ. Geom. 20, 237-266 (1984; Zbl 0556.53001)]. A closed ”sufficiently convex” hypersurface of a Riemannian manifold N can be shrunk by its mean curvature to a small sphere and to a point. ”Sufficiently convex” is specified by a lower bound for the principal curvatures depending on the curvature of N and its derivative.
Reviewer: D.Ferus


53C40 Global submanifolds
53C20 Global Riemannian geometry, including pinching


Zbl 0556.53001
Full Text: DOI EuDML


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