## Meromorphic properties of the resolvent on asymptotically hyperbolic manifolds (2005)

Venue: | Gui05c] [Gui06] [GZ95] [GZ97] [GZ99] [His94] [His00] [Jan79] Colin Guillarmou. Resonances and |

Citations: | 42 - 13 self |

### BibTeX

@INPROCEEDINGS{Guillarmou05meromorphicproperties,

author = {Colin Guillarmou},

title = {Meromorphic properties of the resolvent on asymptotically hyperbolic manifolds},

booktitle = {Gui05c] [Gui06] [GZ95] [GZ97] [GZ99] [His94] [His00] [Jan79] Colin Guillarmou. Resonances and},

year = {2005}

}

### Years of Citing Articles

### OpenURL

### Abstract

Abstract. On an asymptotically hyperbolic manifold (Xn+1, g), Mazzeo and Melrose have constructed the meromorphic extension of the resolvent R(λ): = (∆g − λ(n − λ)) −1 for the Laplacian. However, there are special points on 1 (n − N) that they did not deal with. We 2 show that the points of n − N are at most some poles of finite multiplicity, and that the same 2 property holds for the points of n+1 − N if and only if the metric is ‘even’. On the other 2 hand, there exist some metrics for which R(λ) has an essential singularity on n+1 − N and 2 these cases are generic. At last, to illustrate them, we give some examples with a sequence of poles of R(λ) approaching an essential singularity.