Gradient estimates and the first Neumann eigenvalue on manifolds with boundary

Gradient estimates for eigenfunctions on compact Riemannian manifolds with boundary

The purpose of this paper is to prove the L∞ gradient estimates and L∞ gradient estimates for the unit spectral projection operators of the Dirichlet Laplacian and Neumann (or more general, Ψ1-Robin) Laplacian on compact Riemannian manifolds (M, g) of dimension n ≥ 2 with C2 boundary . And we also get an upper bounds for normal derivatives of the unit spectral projection operators of the Dirich...

The First Dirac Eigenvalue on Manifolds with Positive Scalar Curvature

We show that on every compact spin manifold admitting a Riemannian metric of positive scalar curvature Friedrich’s eigenvalue estimate for the Dirac operator can be made sharp up to an arbitrarily small given error by choosing the metric suitably.

Strichartz Estimates for the Wave Equation on Manifolds with Boundary

Strichartz estimates are well established on flat Euclidean space, where M = R and gij = δij . In that case, one can obtain a global estimate with T = ∞; see for example Strichartz [27], Ginibre and Velo [9], Lindblad and Sogge [16], Keel and Tao [14], and references therein. However, for general manifolds phenomena such as trapped geodesics and finiteness of volume can preclude the development...

Eigenfunction and Bochner Riesz Estimates on Manifolds with Boundary

On Multilinear Spectral Cluster Estimates for Manifolds with Boundary

Let (M, g) be a smooth, compact n-dimensional Riemannian manifold with boundary and let ∆ be the corresponding Laplace-Beltrami operator acting on functions. If the boundary is non-empty, we assume that either Dirichlet or Neumann conditions are imposed along ∂M. Consider the operators χλ defined as projection onto the subspace spanned by the Dirichlet (or Neumann) eigenfunctions whose correspo...