Concerning L^p resolvent estimates for simply connected manifolds of constant curvature

2014/06/08 by Huang, Shanlin, Sogge, Christopher D.
#Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1406.1940

Abstract

We prove families of uniform (L^r,L^s) resolvent estimates for simply connected manifolds of constant curvature (negative or positive) that imply the earlier ones for Euclidean space of Kenig, Ruiz and the second author \citeKRS. In the case of the sphere we take advantage of the fact that the half-wave group of the natural shifted Laplacian is periodic. In the case of hyperbolic space, the key ingredient is a natural variant of the Stein-Tomas restriction theorem.

Related

• On L^p-resolvent estimates and the density of eigenvalues for compact Riemannian manifolds
• On L^p resolvent estimates for elliptic operators on compact manifolds
• L^p - L^q resolvent restriction estimates for submanifolds
• From semiclassical Strichartz estimates to uniform L^p resolvent estimates on compact manifolds
• Endpoint resolvent estimates for compact Riemannian manifolds