KYUNGPOOK Math. J. 2019; 59(2): 341-352
Published online June 23, 2019
Copyright © Kyungpook Mathematical Journal.
Evolution of the First Eigenvalue of Weighted p-Laplacian along the Yamabe Flow
Shahroud Azami
Department of Mathematics, Faculty of Sciences, Imam Khomeini International University, Qazvin, Iran
e-mail : azami@sci.ikiu.ac.ir
Received: July 14, 2018; Accepted: January 21, 2019
Let M be an n-dimensional closed Riemannian manifold with metric g, dμ = e−φ(x)dν be the weighted measure and Δp,φ be the weighted p-Laplacian. In this article we will study the evolution and monotonicity for the first nonzero eigenvalue problem of the weighted p-Laplace operator acting on the space of functions along the Yamabe flow on closed Riemannian manifolds. We find the first variation formula of it along the Yamabe flow. We obtain various monotonic quantities and give an example.
Keywords: Laplace, Yamabe flow, eigenvalue.
