The Semiclassical Resolvent on Conic Manifolds and Application to Schr\"odinger Equations

Abstract

In this article, we shall construct the resolvent of Laplacian at high energies near the spectrum on non-product conic manifolds with a single cone tip. Microlocally, the resolvent kernel is the sum of b-pseudodifferential operators, scattering pseudodifferential operators and intersecting Legendrian distributions. As an application, we shall establish Strichartz estimates for Schr\"odinger equations on non-compact manifolds with multiple non-product conic singularities.