About every convex set in any generic Riemannian manifold

Alexander Lytchak, Anton Petrunin

Research output: Contribution to journalArticlepeer-review

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){(M,g)}. For example, if a convex set in (M,g){(M,g)} is bounded by a smooth hypersurface, then it is strictly convex.

Original languageEnglish (US)
Article number20210058
JournalJournal fur die Reine und Angewandte Mathematik
DOIs
StateAccepted/In press - 2021

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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