Convexity of Hypersurfaces in Spherical Spaces

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dc.creatorRybnikov, Konstantin
dc.date2007-08-23
dc.date2007-10-02
dc.date.accessioned2026-07-07T08:33:03Z
dc.date.available2026-07-07T08:33:03Z
dc.descriptionA spherical set is called convex if for every pair of its points there is at least one minimal geodesic segment that joins these points and lies in the set. We prove that for n >= 3 a complete locally-convex (topological) immersion of a connected (n-1)-manifold into the n-sphere is a surjection onto the boundary of a convex set.
dc.description15 pages, 3 figures. Two more pictures. Corrections, mostly notational have been made. Proofs are given in more detail
dc.identifierhttps://arxiv.org/abs/0708.3149
dc.identifierhttp://arxiv.org/abs/0708.3149
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/138993
dc.subjectMetric Geometry
dc.subjectDifferential Geometry
dc.subject53C45
dc.titleConvexity of Hypersurfaces in Spherical Spaces
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