Comparison formulas for total mean curvatures of Riemannian hypersurfaces

Abstract

We devise some differential forms after Chern to compute a family of formulas for comparing total mean curvatures of nested hypersurfaces in Riemannian manifolds. This yields a quicker proof of a recent result of the author with Joel Spruck, which had been obtained via Reilly’s identities.

Keywords

• quermassintegral
• generalized mean curvature
• chern differential forms
• primary: 53c21
• 53c65
• secondary: 53c42
• 58j05