Eigenvalues Variation of the \(p\)-Laplacian under the Yamabe Flow on SM

Abstract

Let \((M,F)\) be a compact Finsler manifold. Studying geometric flows and the eigenvalues of geometric operators are powerful tools when dealing with geometric problems. In this article we will consider the eigenvalue problem for the p-laplace operator for Sasakian metric acting on the space of functions on SM. We find the first variation formula for the eigenvalues of \(p\)-Laplacian on SM evolving by the Yamabe flow on \(M\) and give some examples.