Resolvent estimates and local decay of waves on conic manifolds Academic Article uri icon

abstract

  • We consider manifolds with conic singularities that are isometric to ℝn outside a compact set. Under natural geometric assumptions on the cone points, we prove the existence of a logarithmic resonance-free region for the cut-off resolvent. The estimate also applies to the exterior domains of non-trapping polygons via a doubling process. The proof of the resolvent estimate relies on the propagation of singularities theorems of Melrose and the second author [23] to establish a “very weak” Huygens’ principle, which may be of independent interest. As applications of the estimate, we obtain a exponential local energy decay and a resonance wave expansion in odd dimensions, as well as a lossless local smoothing estimate for the Schrödinger equation. © 2013 Journal of Differential Geometry. © 2013 Applied Probability Trust.

author list (cited authors)

  • Baskin, D., & Wunsch, J.

citation count

  • 7

publication date

  • October 2013