Evolution and monotonicity of eigenvalues under the Ricci flow

DOI10.1007/s11425-014-4943-7zbMath1327.53084OpenAlexW2075467051MaRDI QIDQ498131

Peng Zhu, Hai-Feng Xu, Shouwen Fang

Publication date: 25 September 2015

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-014-4943-7

zbMATH Keywords

eigenvalueRicci flowWitten-Laplacian

Mathematics Subject Classification ID

Related Items (19)

Evolution and monotonicity of geometric constants along the extended Ricci flow ⋮ Eigenvalues monotonicity of Witten-Laplacian along the mean curvature flow ⋮ On the evolution and monotonicity of first eigenvalues under the Ricci flow ⋮ An upper bound of the heat kernel along the harmonic-Ricci flow ⋮ Monotonicity formulas of eigenvalues and energy functionals along the rescaled List's extended Ricci flow ⋮ Evolution of eigenvalues of geometric operator under the rescaled List's extended Ricci flow ⋮ Unnamed Item ⋮ Monotonicity of eigenvalues and functionals along the Ricci-Bourguignon flow ⋮ Variation of the first eigenvalue of Witten Laplacian and consequences under super Perelman-Ricci flow ⋮ EIGENVALUES OF GEOMETRIC OPERATORS RELATED TO THE WITTEN LAPLACIAN UNDER THE RICCI FLOW ⋮ First Eigenvalues of Geometric Operator under The Ricci-Bourguignon Flow ⋮ Eigenvalues of the weighted Laplacian under the extended Ricci flow ⋮ Estimates and monotonicity of the first eigenvalues under the Ricci flow on closed surfaces ⋮ On the spectra of a family of geometric operators evolving with geometric flows ⋮ Monotonicity formulas for the first eigenvalue of the weighted \(p\)-Laplacian under the Ricci-harmonic flow ⋮ Monotonicity of first eigenvalues along the Yamabe flow ⋮ Evolution of the first eigenvalue of weighted \(p\)-Laplacian along the Ricci-Bourguignon flow ⋮ Monotonicity of eigenvalues of Witten-Laplace operator along the Ricci-bourguignon flow ⋮ Eigenvalues of the Laplace operator with potential under the backward Ricci flow on locally homogeneous \(3\)-manifolds

Cites Work

• The first eigenvalue of \(p\)-Laplace operator under powers of the \(m\)th mean curvature flow
• Entropy and lowest eigenvalue on evolving manifolds
• Eigenvalues of \(\left(-\triangle + \frac{R}{2}\right)\) on manifolds with nonnegative curvature operator
• 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
• The first eigenvalue of the p -Laplace operator under powers of mean curvature flow
• Unnamed Item

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