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arXiv · 1303.5884

An optimal lower curvature bound for convex hypersurfaces in Riemannian manifolds

Stephanie Alexander·Vitali Kapovitch·Anton Petrunin
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Abstract

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

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Stephanie Alexander, Vitali Kapovitch, Anton Petrunin. 2013-03-23. An optimal lower curvature bound for convex hypersurfaces in Riemannian manifolds. https://doi.org/10.1215/ijm/1254403729

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