 

Shahroud Azami
Evolution of the first eigenvalue of weighted pLaplacian along the RicciBourguignon flow
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Published: 
July 14, 2020. 
Keywords: 
Laplace, RicciBourguignon flow, eigenvalue. 
Subject: 
58C40; 53C44, 53C21. 


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


Acknowledgements
N/A


Author information
Shahroud Azami:
Department of Pure Mathematics
Faculty of Science
Imam Khomeini International University
Qazvin, Iran
azami@sci.ikiu.ac.ir

