Resolvent estimates and local decay of waves on conic manifolds

Dean Baskin, Jared Wunsch

Research output: Contribution to journalArticle

9 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)183-214
Number of pages32
JournalJournal of Differential Geometry
Volume95
Issue number2
DOIs
StatePublished - Jan 1 2013

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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