On an Inequality of Andrews, De Lellis, and Topping

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Abstract

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.

Original languageEnglish
Pages (from-to)108-121
Number of pages14
JournalJournal of Geometric Analysis
Volume25
Issue number1
DOIs
Publication statusPublished - 2013 Jan 1

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

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