Geodesic
Closeness to spheres of hypersurfaces with normal curvature bounded below
Sbornik. Mathematics, Tome 204 (2013) no. 11, pp. 1565-1583 Cet article a éte moissonné depuis la source Math-Net.Ru

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For a Riemannian manifold $M^{n+1}$ and a compact domain $\Omega \subset\nobreak M^{n+1}$ bounded by a hypersurface $\partial\Omega$ with normal curvature bounded below, estimates are obtained in terms of the distance from $O$ to $\partial\Omega$ for the angle between the geodesic line joining a fixed interior point $O$ in $\Omega$ to a point on $\partial\Omega$ and the outward normal to the surface. Estimates for the width of a spherical shell containing such a hypersurface are also presented. Bibliography: 9 titles.
Keywords: Riemannian manifold, sectional curvature, normal curvature of a hypersurface, comparison theorems
Mots-clés : $\lambda$-convex hypersurface. 
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A. A. Borisenko; K. D. Drach. Closeness to spheres of hypersurfaces with normal curvature bounded below. Sbornik. Mathematics, Tome 204 (2013) no. 11, pp. 1565-1583. http://geodesic.mathdoc.fr/item/SM_2013_204_11_a1/

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