Resolvent estimates and local decay of waves on conic manifolds

Dean Baskin Northwestern University Jared Wunsch Northwestern University

Differential Geometry mathscidoc:1609.10329

Journal of Differential Geometry, 95, (2), 183-214, 2013
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 Schr¨odinger equation.
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@inproceedings{dean2013resolvent,
  title={RESOLVENT ESTIMATES AND LOCAL DECAY OF WAVES ON CONIC MANIFOLDS},
  author={Dean Baskin, and Jared Wunsch},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160914082013146048991},
  booktitle={Journal of Differential Geometry},
  volume={95},
  number={2},
  pages={183-214},
  year={2013},
}
Dean Baskin, and Jared Wunsch. RESOLVENT ESTIMATES AND LOCAL DECAY OF WAVES ON CONIC MANIFOLDS. 2013. Vol. 95. In Journal of Differential Geometry. pp.183-214. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160914082013146048991.
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