Nobumitsu Nakauchi

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

Abstract 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–Weitzonbeck type which is different from the one for the usual Laplacian.

On the Existence of n-Harmonic Spheres

Using the bubbling argument of Sacks and Uhlenbeck, we prove the existence of n-harmonic maps from the n-sphere to Riemannian manifolds. An application is made to a problem concerning manifolds with strongly pth moment stable stochastic dynamical systems.