EIGENVALUES OF GEOMETRIC OPERATORS RELATED TO THE WITTEN LAPLACIAN UNDER THE RICCI FLOW

DOI10.1017/S0017089516000537zbMath1408.53088MaRDI QIDQ5369122

Peng Zhu, Shouwen Fang, Fei Yang

Publication date: 13 October 2017

Published in: Glasgow Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

normalized Ricci flowevolution of eigenvaluescompact steady Ricci breather

Mathematics Subject Classification ID

Related Items (6)

On the evolution and monotonicity of first eigenvalues under the Ricci flow ⋮ Evolution of eigenvalues of geometric operator under the rescaled List's extended Ricci flow ⋮ Variation of the first eigenvalue of Witten Laplacian and consequences under super Perelman-Ricci flow ⋮ Estimates and monotonicity of the first eigenvalues under the Ricci flow on closed surfaces ⋮ Monotonicity of first eigenvalues along the Yamabe flow ⋮ Eigenvalues of the Laplace operator with potential under the backward Ricci flow on locally homogeneous \(3\)-manifolds

Cites Work

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• Entropy and lowest eigenvalue on evolving manifolds
• Evolution and monotonicity of eigenvalues under the Ricci flow
• A complete proof of the Poincaré and geometrization conjectures -- application of the Hamilton-Perelman theory of the Ricci flow
• Eigenvalues of \(\left(-\triangle + \frac{R}{2}\right)\) on manifolds with nonnegative curvature operator
• Four-manifolds with positive curvature operator
• Ricci solitons on compact three-manifolds
• Three-manifolds with positive Ricci curvature
• Eigenvalues and energy functionals with monotonicity formulae under Ricci flow
• Inequalities for eigenvalues of the drifting Laplacian on Riemannian manifolds
• Eigenvalue monotonicity for the Ricci-Hamilton flow
• Liouville theorems for symmetric diffusion operators on complete Riemannian manifolds
• First eigenvalues of geometric operators under the Ricci flow

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