Some comparisons of Dirichlet, Neumann and buckling eigenvalues on Riemannian manifolds (Q6082870)

In this paper, the authors consider the eigenvalue problems with respect to \(f\)-Laplacian on a bounded domain \(\Omega\) a weighted Riemannian manifold \((M^{n},g, d\sigma)\), where \(f\) is a smooth function defined on \(M^n\), \(d\sigma=e^{-f}dv_{g}\), and the \(f\)-Laplacian is given by \[ \Delta_{f}u=\Delta u-\nabla f\cdot\nabla u. \] The authors study the Dirichlet, Neumann and buckling eigenvalues on Riemannian manifolds. Under some assumptions on Bakry-Émery Ricci curvature, they construct some comparison results on eigenvalues by introducing a new parameter.