Absence of resonance near the critical line on asymptotically hyperbolic spaces
Spectral Theory
2007-05-23 v2 Analysis of PDEs
Differential Geometry
Abstract
As a consequence of a result of Cardoso and Vodev, we show that the resolvent of the Laplacian on asymptotically hyperbolic manifolds is analytic in an exponential neighbourhood of the critical line. The case of non-trapping metrics with constant curvature near infinity is also considered: there exists a strip with at most a finite number of resonances.
Keywords
Cite
@article{arxiv.math/0406496,
title = {Absence of resonance near the critical line on asymptotically hyperbolic spaces},
author = {Colin Guillarmou},
journal= {arXiv preprint arXiv:math/0406496},
year = {2007}
}
Comments
13 pages, slight modifications