%0 Journal Article
%T Some sharp estimates for convex hypersurfaces of pinched normal curvature
%A Kostiantyn Drach
%J Mathematics
%D 2014
%I arXiv
%X For a convex domain $D$ bounded by the hypersurface $\partial D$ in a space of constant curvature we give sharp bounds on the width $R-r$ of a spherical shell with radii $R$ and $r$ that can enclose $\partial D$, provided that normal curvatures of $\partial D$ are pinched by two positive constants. Furthermore, in the Euclidean case we also present sharp estimates for the quotient $R/r$. From the obtained estimates we derive stability results for almost umbilical hypersurfaces in the constant curvature spaces.
%U http://arxiv.org/abs/1402.2685v2