Some sharp estimates for convex hypersurfaces of pinched normal curvature

Kostiantyn Drach

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arXiv · 1402.2685

Some sharp estimates for convex hypersurfaces of pinched normal curvature

Kostiantyn Drach

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Abstract

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.

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Kostiantyn Drach. 2014-02-11. Some sharp estimates for convex hypersurfaces of pinched normal curvature. https://arxiv.org/abs/1402.2685

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