Monotonicity formulas for the first eigenvalue of the weighted p-Laplacian under the Ricci-harmonic flow
Abstract Let Δp,ϕ $\Delta _{p,\phi }$ be the weighted p-Laplacian defined on a smooth metric measure space. We study the evolution and monotonicity formulas for the first eigenvalue, λ1=λ(Δp,ϕ) $\lambda _{1}=\lambda (\Delta _{p,\phi })$, of Δp,ϕ $\Delta _{p,\phi }$ under the Ricci-harmonic flow. We...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2019-01-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-019-1961-6 |
| Summary: | Abstract Let Δp,ϕ $\Delta _{p,\phi }$ be the weighted p-Laplacian defined on a smooth metric measure space. We study the evolution and monotonicity formulas for the first eigenvalue, λ1=λ(Δp,ϕ) $\lambda _{1}=\lambda (\Delta _{p,\phi })$, of Δp,ϕ $\Delta _{p,\phi }$ under the Ricci-harmonic flow. We derive some monotonic quantities involving the first eigenvalue, and as a consequence, this shows that λ1 $\lambda _{1}$ is monotonically nondecreasing and almost everywhere differentiable along the flow existence. |
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| ISSN: | 1029-242X |