About every convex set in any generic Riemannian manifold

Alexander Lytchak; Anton Petrunin

doi:10.1515/crelle-2021-0058

About every convex set in any generic Riemannian manifold

Alexander Lytchak
, Anton Petrunin

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

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 language	English (US)
Pages (from-to)	235-245
Number of pages	11
Journal	Journal fur die Reine und Angewandte Mathematik
Volume	2022
Issue number	782
DOIs	https://doi.org/10.1515/crelle-2021-0058
State	Published - Jan 1 2022

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1515/crelle-2021-0058

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

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AB - 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.

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About every convex set in any generic Riemannian manifold

Abstract

All Science Journal Classification (ASJC) codes

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