TY - JOUR
T1 - About every convex set in any generic Riemannian manifold
AU - Lytchak, Alexander
AU - Petrunin, Anton
N1 - Publisher Copyright:
© 2021 Walter de Gruyter GmbH, Berlin/Boston 2022.
PY - 2022/1/1
Y1 - 2022/1/1
N2 - 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.
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.
UR - http://www.scopus.com/inward/record.url?scp=85118482606&partnerID=8YFLogxK
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U2 - 10.1515/crelle-2021-0058
DO - 10.1515/crelle-2021-0058
M3 - Article
AN - SCOPUS:85118482606
SN - 0075-4102
VL - 2022
SP - 235
EP - 245
JO - Journal fur die Reine und Angewandte Mathematik
JF - Journal fur die Reine und Angewandte Mathematik
IS - 782
ER -