Geodesic
Closeness to spheres of hypersurfaces with normal curvature bounded below
Sbornik. Mathematics, Tome 204 (2013) no. 11, pp. 1565-1583

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{SM_2013_204_11_a1,
     author = {A. A. Borisenko and K. D. Drach},
     title = {Closeness to spheres of hypersurfaces with normal curvature bounded below},
     journal = {Sbornik. Mathematics},
     pages = {1565--1583},
     publisher = {mathdoc},
     volume = {204},
     number = {11},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2013_204_11_a1/}
}
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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/