Meromorphic Properties of the Resolvent on Asymptotically Hyperbolic Manifolds

@inproceedings{GUILLARMOU2003MeromorphicPO,
  title={Meromorphic Properties of the Resolvent on Asymptotically Hyperbolic Manifolds},
  author={COLIN GUILLARMOU},
  year={2003}
}
  • COLIN GUILLARMOU
  • 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
Highly Influential
This paper has highly influenced 14 other papers. REVIEW HIGHLY INFLUENTIAL CITATIONS
Highly Cited
This paper has 77 citations. REVIEW CITATIONS

From This Paper

Figures, tables, and topics from this paper.

Citations

Publications citing this paper.

77 Citations

051015'07'10'13'16
Citations per Year
Semantic Scholar estimates that this publication has 77 citations based on the available data.

See our FAQ for additional information.

References

Publications referenced by this paper.
Showing 1-10 of 16 references

Scattering matrix in conformal geometry

  • L. Guillopé
  • Invent . Math .
  • 2003

The divisor of Selberg ’ s zeta function for Kleinian groups ,

  • P. Perry
  • Duke Math . J .
  • 2001

A perturbation theory for resonances

  • S. Agmon
  • Comm . Pure . Appl . Math .
  • 1998

Polynomial bounds on the number of resonances for some complete spaces of constant negative curvature near infinity

  • M. Zworski L. Guillopé
  • Asymp . Anal .
  • 1995

Upper bounds on the number of resonances for non - compact complete Riemann surfaces

  • M. Zworski L. Guillopé
  • J . Funct . Anal .
  • 1995

Fonctions Zêta de Selberg et surfaces de géométrie finie , Adv

  • M. Zworski L. Guillopé
  • Stud . Pure Math .
  • 1992

Unique continuation at infinity and embedded eigenvalues for asymptotically hyperbolic manifolds

  • R. Mazzeo
  • American J . Math .
  • 1991

The Selberg Zeta function and a local trace formula for Kleinian groups

  • A. Sá Barreto, M. Zworski
  • J . Reine Angew . Math .
  • 1990

Similar Papers

Loading similar papers…