paper

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