Uniform Sobolev Resolvent Estimates for the Laplace–Beltrami Operator on Compact Manifolds

Uniform Estimates of the Resolvent of the Laplace–Beltrami Operator on Infinite Volume Riemannian Manifolds with Cusps.II

We prove uniform weighted high frequency estimates for the resolvent of the Laplace-Beltrami operator on connected infinite volume Riemannian manifolds under some natural assumptions on the metric on the ends of the manifold. This extends previous results by Burq [3] and Vodev [8].

On L-resolvent Estimates and the Density of Eigenvalues for Compact Riemannian Manifolds

We address an interesting question raised by Dos Santos Ferreira, Kenig and Salo [11] about regions Rg ⊂ C for which there can be uniform L 2n n+2 → L 2n n−2 resolvent estimates for ∆g + ζ, ζ ∈ Rg , where ∆g is the Laplace-Beltrami operator with metric g on a given compact boundaryless Riemannian manifold of dimension n ≥ 3. This is related to earlier work of Kenig, Ruiz and the third author [1...

ON Lp RESOLVENT ESTIMATES FOR LAPLACE-BELTRAMI OPERATORS ON COMPACT MANIFOLDS

In this article we prove L estimates for resolvents of Laplace-Beltrami operators on compact Riemannian manifolds, generalizing results of [12] in the Euclidean case and [17] for the torus. We follow [18] and construct Hadamard’s parametrix, then use classical boundedness results on integral operators with oscillatory kernels related to the Carleson and Sjölin condition. Our initial motivation ...

Resolvent Estimates of the Dirac Operator

Resolvent Estimates and Local Decay of Waves on Conic Manifolds

We consider manifolds with conic singularites that are isometric to R outside a compact set. Under natural geometric assumptions on the cone points, we prove the existence of a logarithmic resonancefree region for the cut-off resolvent. The estimate also applies to the exterior domains of non-trapping polygons via a doubling process. The proof of the resolvent estimate relies on the propagation...