Absence of resonance near the critical line on asymptotically hyperbolic spaces

Article type: Research Article

Authors: Guillarmou, Colin

Affiliations: Laboratoire de Mathématiques Jean Leray, UMR 6629 CNRS/Université de Nantes, 2, rue de la Houssinière, BP 92208, 44322 Nantes cedex 03, France E‐mail: cguillar@math.univ‐nantes.fr

Abstract: As a consequence of a result of Cardoso–Vodev, we show that the resolvent of the Laplacian on asymptotically hyperbolic manifolds is analytic in an exponential neighbourhood of the critical line $\{\Re(\lambda )=\frac{n}{2}\}$. The case of non‐trapping metrics with constant curvature near infinity is also considered: there is a strip $\{\Re(\lambda )>\frac{n}{2}-\varepsilon\}$ with a finite number of resonances.

Journal: Asymptotic Analysis, vol. 42, no. 1-2, pp. 105-121, 2005