About every convex set in any generic Riemannian manifold

Abstract

We give a necessary condition on a geodesic in a Riemannian manifold that can run in some convex hypersurface. As a corollary we obtain peculiar properties that hold true for every convex set in any generic Riemannian manifold (M,g). For example, if a convex set in (M,g) is bounded by a smooth hypersurface, then it is strictly convex.

10 pages, 2 figures

Cited by in corpus (1)

• A non-compact convex hull in generalized non-positive curvature