Abolarinwa, Abimbola (2019) Eigenvalues of the weighted Laplacian under the extended Ricci flow. Advances in Geometry, 19 (1). pp. 131-143. ISSN 1615-7168, 1615-715X
Full text not available from this repository.Abstract
Let ∆φ = ∆ − ∇φ∇ be a symmetric diffusion operator with an invariant weighted volume measure dμ = e−φ dν on an n-dimensional compact Riemannian manifold (M, g), where g = g(t) solves the extended Ricci flow. We study the evolution and monotonicity of the first nonzero eigenvalue of ∆φ and we obtain several monotone quantities along the extended Ricci flow and its volume preserving version under some technical assumption. We also show that the eigenvalues diverge in a finite time for n ≥ 3. Our results are natural extensions of some known results for Laplace–Beltrami operators under various geometric flows.
| Item Type: | Article |
|---|---|
| Subjects: | Q Science > QC Physics |
| Depositing User: | Mr DIGITAL CONTENT CREATOR LMU |
| Date Deposited: | 17 Apr 2019 11:14 |
| Last Modified: | 17 Apr 2019 11:14 |
| URI: | https://eprints.lmu.edu.ng/id/eprint/2104 |
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