Illinois Journal of Mathematics

An optimal lower curvature bound for convex hypersurfaces in Riemannian manifolds

Stephanie Alexander, Vitali Kapovitch, and Anton Petrunin

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It is proved that a convex hypersurface in a Riemannian manifold of sectional curvature $\ge\kappa$ is an Alexandrov's space of curvature $\ge\kappa$. This theorem provides an optimal lower curvature bound for an older theorem of Buyalo.

Article information

Illinois J. Math., Volume 52, Number 3 (2008), 1031-1033.

First available in Project Euclid: 1 October 2009

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Zentralblatt MATH identifier

Primary: 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20] 53B25: Local submanifolds [See also 53C40]
Secondary: 53C23: Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces 53C45: Global surface theory (convex surfaces à la A. D. Aleksandrov)


Alexander, Stephanie; Kapovitch, Vitali; Petrunin, Anton. An optimal lower curvature bound for convex hypersurfaces in Riemannian manifolds. Illinois J. Math. 52 (2008), no. 3, 1031--1033. doi:10.1215/ijm/1254403729.

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