Scattering poles for asymptotically hyperbolic manifolds

David Borthwick, Peter Perry

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


For a class of manifolds X that includes quotients of real hyperbolic (n + 1)-dimensional space by a convex co-compact discrete group, we show that the resonances of the meromorphically continued resolvent kernel for the Laplacian on X coincide, with multiplicities, with the poles of the meromorphically continued scattering operator for X. In order to carry out the proof, we use Shmuel Agmon's perturbation theory of resonances to show that both resolvent resonances and scattering poles are simple for generic potential perturbations.

Original languageEnglish
Pages (from-to)1215-1231
Number of pages17
JournalTransactions of the American Mathematical Society
Issue number3
StatePublished - 2002


  • Hyperbolic manifolds
  • Scattering resonances

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics


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