Open Access
October 2013 Resolvent estimates and local decay of waves on conic manifolds
Dean Baskin, Jared Wunsch
J. Differential Geom. 95(2): 183-214 (October 2013). DOI: 10.4310/jdg/1376053445


We consider manifolds with conic singularities that are isometric to $\mathbb{R}^n$ 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 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.


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Dean Baskin. Jared Wunsch. "Resolvent estimates and local decay of waves on conic manifolds." J. Differential Geom. 95 (2) 183 - 214, October 2013.


Published: October 2013
First available in Project Euclid: 9 August 2013

zbMATH: 1296.53075
MathSciNet: MR3128982
Digital Object Identifier: 10.4310/jdg/1376053445

Rights: Copyright © 2013 Lehigh University

Vol.95 • No. 2 • October 2013
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