A generalization of almost-Schur lemma for closed Riemannian manifolds

DOI10.1007/s10455-012-9339-8zbMath1276.53054OpenAlexW2108652067WikidataQ115384593 ScholiaQ115384593MaRDI QIDQ1941762

Xu Cheng

Publication date: 21 March 2013

Published in: Annals of Global Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10455-012-9339-8

zbMATH Keywords

Schur lemmaEinstein manifoldeigenvalue of Laplace operator

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25)

Related Items (15)

A note on the almost-Schur lemma on smooth metric measure spaces ⋮ Deformation of the \(\sigma_2\)-curvature ⋮ A symmetric 2-tensor canonically associated to \(Q\)-curvature and its applications ⋮ Almost Schur lemma for manifolds with boundary ⋮ Some De Lellis-Topping type inequalities and their applications on an NCC Riemannian triple with boundary ⋮ De Lellis-Topping type inequalities on smooth metric measure spaces ⋮ Some almost-Schur type inequalities and applications on sub-static manifolds ⋮ Rigidity for closed totally umbilical hypersurfaces in space forms ⋮ De Lellis-Topping type inequalities for smooth metric measure spaces ⋮ Pinching of the first eigenvalue for second order operators on hypersurfaces of the Euclidean space ⋮ On an inequality of Andrews, De Lellis, and Topping ⋮ Some almost-Schur type inequalities for \(k\)-Bakry-Emery Ricci tensor ⋮ Optimal constants of \(L^2\) inequalities for closed nearly umbilical hypersurfaces in space forms ⋮ De Lellis–Topping type inequalities for $f$-Laplacians ⋮ De Lellis-Topping inequalities on weighted manifolds with boundary

Cites Work

• Unnamed Item
• Rigidity for closed totally umbilical hypersurfaces in space forms
• Almost-Schur lemma
• Optimal rigidity estimates for nearly umbilical surfaces
• On problems related to an inequality of Andrews, De Lellis, and Topping
• An almost Schur theorem on 4-dimensional manifolds
• The Exponential Decay Rate of the Lower Bound for the First Eigenvalue of Compact Manifolds

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