Lower bounds for the first eigenvalue of the \(p\)-Laplacian on compact manifolds with positive Ricci curvature (Q881612)

The first eigenvalue of the \(p\)-Laplace operator associated with a Riemannian metric on a compact manifold is studied. The author investigates its lower bound in terms of some geometric quantities such as the diameter and the inscribed radius when the Ricci curvature is positive or non-negative. The other eigenvalue problem associated with the \(p\)-Laplacian that is considered is the Dirichlet problem for compact manifolds with boundary with some proper geometric hypotheses.