Gradient and Hessian Estimates for Dirichlet and Neumann Eigenfunctions

Abstract

We establish integral formulas and sharp two-sided bounds for the Ricci curvature, mean curvature and second fundamental form on a Riemannian manifold with boundary. As applications, sharp gradient and Hessian estimates are derived for the Dirichlet and Neumann eigenfunctions.

15 pages

References in corpus (1)

• Identifying Constant Curvature Manifolds, Einstein Manifolds, and Ricci Parallel Manifolds