Continuity of total curvatures of Riemannian hypersurfaces

2025/11/20 by Ghomi, Mohammad
#53C24 #53C65 #Differential Geometry (math.DG) #FOS: Mathematics #Primary: 53C21 #Secondary: 52A20

paper · doi:10.48550/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.

Citations

• Comparison formulas for total mean curvatures of Riemannian hypersurfaces
• Minkowski inequality in Cartan-Hadamard manifolds
• Total mean curvatures of Riemannian hypersurfaces
• Total curvature and the isoperimetric inequality in Cartan-Hadamard manifolds

Related

• Total mean curvatures of Riemannian hypersurfaces
• Minkowski inequality in Cartan-Hadamard manifolds
• Higher order mean curvature estimates for bounded complete hypersurfaces
• Total curvature and the isoperimetric inequality in Cartan-Hadamard manifolds
• Convexity and rigidity of hypersurfaces in Cartan-Hadamard manifolds