It is proved that a convex hypersurface in a Riemannian manifold of sectional curvature ≥κ is an Alexandrov’s space of curvature ≥κ. This theorem provides an optimal lower curvature bound for an older theorem of Buyalo.
Publié le : 2008-05-15
Classification:
53C20,
53B25,
53C23,
53C45
@article{1254403729,
author = {Alexander, Stephanie and Kapovitch, Vitali and Petrunin, Anton},
title = {An optimal lower curvature bound for convex hypersurfaces in Riemannian manifolds},
journal = {Illinois J. Math.},
volume = {52},
number = {1},
year = {2008},
pages = { 1031-1033},
language = {en},
url = {http://dml.mathdoc.fr/item/1254403729}
}
Alexander, Stephanie; Kapovitch, Vitali; Petrunin, Anton. An optimal lower curvature bound for convex hypersurfaces in Riemannian manifolds. Illinois J. Math., Tome 52 (2008) no. 1, pp. 1031-1033. http://gdmltest.u-ga.fr/item/1254403729/