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The Journal of Geometric Analysis

, Volume 25, Issue 2, pp 1185–1210 | Cite as

Compactness of Relatively Isospectral Sets of Surfaces Via Conformal Surgeries

  • Pierre AlbinEmail author
  • Clara L. Aldana
  • Frédéric Rochon
Article

Abstract

We introduce a notion of relative isospectrality for surfaces with boundary having possibly non-compact ends either conformally compact or asymptotic to cusps. We obtain a compactness result for such families via a conformal surgery that allows us to reduce to the case of surfaces hyperbolic near infinity recently studied by Borthwick and Perry, or to the closed case by Osgood, Phillips, and Sarnak if there are only cusps.

Keywords

Inverse spectral problem Analytic surgery Hyperbolic cusps Hyperbolic funnels Relatively isospectral 

Mathematics Subject Classification

58J53 57R65 58G11 35P20 

Notes

Acknowledgements

The authors are grateful to David Borthwick, Gilles Carron, Andrew Hassell, Rafe Mazzeo, and Richard Melrose for helpful conversations and to the anonymous referee for their comments.

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Copyright information

© Mathematica Josephina, Inc. 2013

Authors and Affiliations

  • Pierre Albin
    • 1
    Email author
  • Clara L. Aldana
    • 2
  • Frédéric Rochon
    • 3
  1. 1.Department of MathematicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  2. 2.Max Planck Institut für Gravitationsphysik (AEI)GolmGermany
  3. 3.Département de MathématiquesUQÀMMontréalCanada

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