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 language | English (US) |
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Pages (from-to) | 183-214 |
Number of pages | 32 |
Journal | Journal of Differential Geometry |
Volume | 95 |
Issue number | 2 |
DOIs | |
State | Published - 2013 |
ASJC Scopus subject areas
- Analysis
- Algebra and Number Theory
- Geometry and Topology