The diffractive wave trace on manifolds with conic singularities

DOI10.1016/j.aim.2016.09.013zbMath1378.53050arXiv1411.6913OpenAlexW2964244231MaRDI QIDQ329534

Jared Wunsch, G. Austin Ford

Publication date: 21 October 2016

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.6913

zbMATH Keywords

wave equationconediffractionconic singularitywave trace

Mathematics Subject Classification ID

Groups and semigroups of linear operators (47D03) Elliptic equations on manifolds, general theory (58J05) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (11)

On non-diffractive cones ⋮ Vacuum isolating and blow-up analysis for edge hyperbolic system on edge Sobolev spaces ⋮ The Neumann isospectral problem for trapezoids ⋮ Invariance solutions and blow-up property for edge degenerate pseudo-hyperbolic equations in edge Sobolev spaces ⋮ A quantitative Vainberg method for black box scattering ⋮ Diffractive propagation on conic manifolds ⋮ On resonances generated by conic diffraction ⋮ Diffraction of the Aharonov-Bohm Hamiltonian ⋮ The wave trace and resonances of the magnetic Hamiltonian with singular vector potentials ⋮ Propagation of polyhomogeneity, diffraction, and scattering on product cones ⋮ Resonance-free regions for diffractive trapping by conormal potentials

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Resolvent estimates and local decay of waves on conic manifolds
• The analysis of linear partial differential operators. III: Pseudo-differential operators
• Propagation of singularities for the wave equation on edge manifolds
• A new formula for the shape operator of a geodesic sphere and its applications
• Transformation of boundary problems
• The spectrum of positive elliptic operators and periodic bicharacteristics
• On the wave equation on a compact Riemannian manifold without conjugate points
• Complex powers of differential operators on manifolds with conical singularities
• Strichartz estimates for the wave and Schrödinger equations with the inverse-square potential
• A Poisson relation for conic manifolds.
• Formule de Poisson pour les variétés riemanniennes
• Propagation of singularities for the wave equation on conic manifolds
• The spectral function of an elliptic operator
• Fourier integral operators. I
• Contribution of periodic diffractive geodesics
• On the diffraction of waves by conical singularities. I
• On the diffraction of waves by conical singularities. II
• Strichartz Estimates for the Wave Equation on Flat Cones
• Riemannian geometry and geometric analysis

This page was built for publication: The diffractive wave trace on manifolds with conic singularities