Evolution and monotonicity of the first eigenvalue of p-Laplacian under the Ricci-harmonic flow
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Abimbola Abolarinwa
Abstract
We study the evolution and monotonicity of the eigenvalues of p-Laplace operator on an m-dimensional compact Riemannian manifold M whose metric g(t) evolves by the Ricci-harmonic flow. The first nonzero eigenvalue is proved to be monotonically nondecreasing along the flow and differentiable almost everywhere. As a corollary, we recover the corresponding results for the usual Laplace–Beltrami operator when p = 2. We also examine the evolution and monotonicity under volume preserving flow and it turns out that the first eigenvalue is not monotone in general.
Funding source: Osun State College of Technology, Nigeria
Award Identifier / Grant number: TETFund
The author wishes to thank the anonymous referees for their useful comments and suggestions.
© 2015 by De Gruyter
Articles in the same Issue
- Frontmatter
- Approximation of common fixed points of left Bregman strongly nonexpansive mappings and solutions of equilibrium problems
- Global existence and stability results for partial fractional random differential equations
- One-phase Stefan problem with temperature-dependent thermal conductivity and a boundary condition of Robin type
- On Janowski harmonic functions
- Oscillation results for higher order nonlinear neutral differential equations with positive and negative coefficients
- Averaging of a nonlinear bipolar model with phase transition and oscillating external forces
- Evolution and monotonicity of the first eigenvalue of p-Laplacian under the Ricci-harmonic flow
Articles in the same Issue
- Frontmatter
- Approximation of common fixed points of left Bregman strongly nonexpansive mappings and solutions of equilibrium problems
- Global existence and stability results for partial fractional random differential equations
- One-phase Stefan problem with temperature-dependent thermal conductivity and a boundary condition of Robin type
- On Janowski harmonic functions
- Oscillation results for higher order nonlinear neutral differential equations with positive and negative coefficients
- Averaging of a nonlinear bipolar model with phase transition and oscillating external forces
- Evolution and monotonicity of the first eigenvalue of p-Laplacian under the Ricci-harmonic flow
