New York Journal of Mathematics
Volume 26 (2020), 735-755


Shahroud Azami

Evolution of the first eigenvalue of weighted p-Laplacian along the Ricci-Bourguignon flow

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Published: July 14, 2020.
Keywords: Laplace, Ricci-Bourguignon flow, eigenvalue.
Subject: 58C40; 53C44, 53C21.

Let M be an n-dimensional closed Riemannian manifold with metric g. Let
dμ=e-φ(x)dν be the weighted measure and Δp,φ be the weighted p-Laplacian. In this article we will investigate monotonicity for the first eigenvalue problem of the weighted p-Laplace operator acting on the space of functions along the Ricci-Bourguignon flow on closed Riemannian manifolds. We find the first variation formula for the eigenvalues of the weighted p-Laplacian on a closed Riemannian manifold evolving by the Ricci-Bourguignon flow and we obtain various monotonic quantities. At the end we find some applications in 2-dimensional and 3-dimensional manifolds and give an example.



Author information

Shahroud Azami:
Department of Pure Mathematics
Faculty of Science
Imam Khomeini International University
Qazvin, Iran