The diffractive wave trace on manifolds with conic singularities

G. Austin Ford, Jared Wunsch*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Let (X,g) be a compact manifold with conic singularities. Taking Δg to be the Friedrichs extension of the Laplace–Beltrami operator, we examine the singularities of the trace of the half-wave group e−itΔg arising from strictly diffractive closed geodesics. Under a generic nonconjugacy assumption, we compute the principal amplitude of these singularities in terms of invariants associated to the geodesic and data from the cone point. This generalizes the classical theorem of Duistermaat–Guillemin on smooth manifolds and a theorem of Hillairet on flat surfaces with cone points.

Original languageEnglish (US)
Pages (from-to)1330-1385
Number of pages56
JournalAdvances in Mathematics
Volume304
DOIs
StatePublished - Jan 2 2017

Keywords

  • Cone
  • Conic singularity
  • Diffraction
  • Wave equation
  • Wave trace

ASJC Scopus subject areas

  • Mathematics(all)

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