An optimal lower curvature bound for convex hypersurfaces in Riemannian manifolds

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.

3 pages

Cited by in corpus (5)

• Semiconcave functions in Alexandrov's geometry
• The behavior of harmonic functions at singular points of $\mathsf{RCD}$ spaces
• Curvature tensor of smoothable Alexandrov spaces
• The $L^p$-Calderón-Zygmund inequality on non-compact manifolds of positive curvature
• Hyperbolization of cusps with convex boundary