Compactness of Relatively Isospectral Sets of Surfaces Via Conformal Surgeries

Pierre Albin, Clara L. Aldana, Frédéric Rochon

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)1185-1210
Number of pages26
JournalJournal of Geometric Analysis
Volume25
Issue number2
DOIs
StatePublished - Apr 2015

Keywords

  • Analytic surgery
  • Hyperbolic cusps
  • Hyperbolic funnels
  • Inverse spectral problem
  • Relatively isospectral

ASJC Scopus subject areas

  • Geometry and Topology

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