On resonances generated by conic diffraction

Luc Hillairet, Jared Wunsch

Research output: Contribution to journalArticlepeer-review

Abstract

We describe the resonances closest to the real axis generated by diffraction of waves among cone points on a manifold with Euclidean ends. These resonances lie asymptotically evenly spaced along a curve of the form Im λ log |Re λ| = −ν; here ν = (n − 1)/2L0 where n is the dimension and L0 is the length of the longest geodesic connecting two cone points. Moreover there are asymptotically no resonances below this curve and above the curve Im λ log |Re λ| = −Λ for a fixed Λ > ν.

Original languageEnglish (US)
Pages (from-to)1715-1752
Number of pages38
JournalAnnales de l'Institut Fourier
Volume70
Issue number4
DOIs
StatePublished - 2020

Keywords

  • Conic singularities
  • Diffraction
  • Resonances
  • Scattering
  • Wave propagation

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

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