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arXiv · 2103.15189

About every convex set in any generic Riemannian manifold

Alexander Lytchak·Anton Petrunin
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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.

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Alexander Lytchak, Anton Petrunin. 2021-03-28. About every convex set in any generic Riemannian manifold. https://doi.org/10.1515/crelle-2021-0058

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