First eigenvalue monotonicity for the \(p\)-Laplace operator under the Ricci flow

DOI10.1007/S10114-011-8565-5zbMath1306.58003OpenAlexW2169348284MaRDI QIDQ475770

Jia-Yong Wu

Publication date: 27 November 2014

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-011-8565-5

zbMATH Keywords

monotonicityRicci flowfirst eigenvalue\(p\)-Laplace operator

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Spectral theory; eigenvalue problems on manifolds (58C40)

Related Items (20)

Eigenvalues monotonicity of Witten-Laplacian along the mean curvature flow ⋮ Monotonicity formulas of eigenvalues and energy functionals along the rescaled List's extended Ricci flow ⋮ Eigenvalues under the backward Ricci flow on locally homogeneous closed 3-manifolds ⋮ Unnamed Item ⋮ The first eigenvalue of \(p\)-Laplace operator under powers of the \(m\)th mean curvature flow ⋮ Unnamed Item ⋮ Evolution of the Steklov eigenvalue under geodesic curvature flow ⋮ Evolution of the first eigenvalue along the inverse mean curvature flow in space forms ⋮ First eigenvalues of free boundary hypersurfaces in the unit ball along the inverse mean curvature flow ⋮ Yamabe Flow On Nilpotent Lie Groups ⋮ Eigenvalue monotonicity of $(p,q)$-Laplacian along the Ricci-Bourguignon flow ⋮ First Eigenvalues of Geometric Operator under The Ricci-Bourguignon Flow ⋮ The first eigenvalue of the p -Laplace operator under powers of mean curvature flow ⋮ Evolution of the first eigenvalue of the clamped plate on manifold along the Ricci flow ⋮ Eigenvalues variation of the p-Laplacian under the Yamabe flow ⋮ Evolution of the first eigenvalue of the Laplace operator and the \(p\)-Laplace operator under a forced mean curvature flow ⋮ On the spectrum of the \(p\)-biharmonic operator under the Ricci flow ⋮ Monotonicity formulas for the first eigenvalue of the weighted \(p\)-Laplacian under the Ricci-harmonic 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

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Eigenvalues of \(\left(-\triangle + \frac{R}{2}\right)\) on manifolds with nonnegative curvature operator
• Some results on subelliptic equations
• Notes on Perelman's papers
• Regularity for a more general class of quasilinear equations
• The first eigenvalue of the \(p\)-Laplacian on a compact Riemannian manifold.
• Three-manifolds with positive Ricci curvature
• First eigenvalue for the \(p\)-Laplace operator
• Eigenvalues and energy functionals with monotonicity formulae under Ricci flow
• Local behavior of solutions of quasi-linear equations
• Eigenvalue monotonicity for the Ricci-Hamilton flow
• \(p\)-Laplace operator and diameter of manifolds
• First eigenvalues of geometric operators under the Ricci flow
• Local gradient estimates of $p$-harmonic functions, $1/H$-flow, and an entropy formula

This page was built for publication: First eigenvalue monotonicity for the \(p\)-Laplace operator under the Ricci flow