Meromorphic Properties of the Resolvent on Asymptotically Hyperbolic Manifolds

  title={Meromorphic Properties of the Resolvent on Asymptotically Hyperbolic Manifolds},
  • Published 2003
On an asymptotically hyperbolic manifold (X n+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 2 (n − N) that they did not deal with. We show that the points of n 2 − N are at most some poles of finite multiplicity, and that the same property holds for the points of n+1 2 − N if and only if the metric is 'even'. On the other hand, there exist some metrics for which R(λ) has… CONTINUE READING
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