The first eigenvalue of the p-Laplacian on a compact Riemannian manifold Original Research Article

The first nonlinear eigenvalue of the p-Laplacian (p⩾2) is investigated for a compact manifold of nonnegative Ricci curvature with or without boundary. Lower bound estimates are given by the diameter or the inscribed radius. The key ingredients in proofs are the formula of Bochner–Weitzönbeck type which is different from the one for the usual Laplacian.