On an inequality of Andrews, De Lellis and Topping

Abstract

Using the method of De Lellis-Topping, we prove some almost Schur type results. For example, one of our results gives a quantitative measure of how close the higher mean curvature of a submanifold is to its average value. We also derive another sharp Andrews-De Lellis-Topping type inequality involving the Riemannian curvature tensor and discuss its equality case.

15 pages. Minor typos corrected and references updated. To appear in Journal of Geometric Analysis

References in corpus (1)

• Rigidity for nearly umbilical hypersurfaces in space forms