Continuity of total curvatures of Riemannian hypersurfaces
arXiv:2511.15955
Abstract
We show that total generalized mean curvatures of hypersurfaces with positive reach in Riemannian manifolds, and convex bodies in Cartan-Hadamard spaces, are continuous with respect to Hausdorff distance.
8 pages; Minor revisions; Accepted for publication in Proceedings of AMS