Absence of resonance near the critical line on asymptotically hyperbolic spaces

Details Absence of resonance near the critical line on asymptotically hyperbolic spaces Absence of resonance near the critical line on asymptotically hyperbolic spaces

2004-06-24

arxiv.org/abs/math/0406496v2

Asymptot. Anal. 42 (2005), no. 1-2, 105--121

Mathematics

Spectral Theory

13 pages, slight modifications

Scientific paper

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.

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