Curvature tensor of smoothable Alexandrov spaces

Abstract

We prove weak convergence of curvature tensors of Riemannian manifolds for converging noncollapsing sequences with a lower bound on sectional curvature.

34 pages, 4 figures

References in corpus (3)

• Semiconcave functions in Alexandrov's geometry
• Convergence of pointed non-compact metric measure spaces and stability of Ricci curvature bounds and heat flows
• An optimal lower curvature bound for convex hypersurfaces in Riemannian manifolds

Cited by in corpus (3)

• Stability of Tori under Lower Sectional Curvature
• On manifolds with almost non-negative Ricci curvature and integrally-positive $k^{th}$-scalar curvature
• A lower bound for the curvature integral under an upper curvature bound