High Energy Resolvent Estimates on Conformally Compact Manifolds with Variable Curvature at Infinity
Analysis of PDEs
2015-11-19 v1 Spectral Theory
Abstract
We construct a semiclassical parametrix for the resolvent of the Laplacian acing on functions on non-trapping conformally compact manifolds with variable sectional curvature at infinity, we use it to prove high energy resolvent estimates and to show existence of resonance free strips of arbitrary height away from the imaginary axis. We then use the results of Datchev and Vasy on gluing semiclassical resolvent estimates to extend these results to conformally compact manifolds with normal hyperbolic trapping.
Keywords
Cite
@article{arxiv.1511.05891,
title = {High Energy Resolvent Estimates on Conformally Compact Manifolds with Variable Curvature at Infinity},
author = {Antonio Sa Barreto and Yiran Wang},
journal= {arXiv preprint arXiv:1511.05891},
year = {2015}
}