Absence of resonance near the critical line on asymptotically hyperbolic spaces

2004/06/30 by Colin Guillarmou · 1 citation
Mathematics · #math.SP #math.AP #math.DG #msc:58J50 #msc:35P25

paper · pdf

published as Asymptot. Anal. 42 (2005), no. 1-2, 105--121 · 13 pages, slight modifications

arxiv created 2005/09/02 · arxiv updated 2009/12/01

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.

Cited by

• The High Energy Distribution of Scattering Phase Shifts of Schrödinger operators in Hyperbolic Space

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