Universität zu Köln

Lytchak, Alexander and Petrunin, Anton (2022). About every convex set in any generic Riemannian manifold. J. Reine Angew. Math., 2022 (782). S. 235 - 246. BERLIN: WALTER DE GRUYTER GMBH. ISSN 1435-5345

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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.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Lytchak, Alexander UNSPECIFIED UNSPECIFIED UNSPECIFIED Petrunin, Anton UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-672327
DOI:	10.1515/crelle-2021-0058
Journal or Publication Title:	J. Reine Angew. Math.
Volume:	2022
Number:	782
Page Range:	S. 235 - 246
Date:	2022
Publisher:	WALTER DE GRUYTER GMBH
Place of Publication:	BERLIN
ISSN:	1435-5345
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/67232