Using the method of De Lellis–Topping (Calculus of Variations and Partial Differential Equations, pp. 1–8, 2012), 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.
All Science Journal Classification (ASJC) codes
- Geometry and Topology