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- W4226110007 abstract "In this paper, we study the problem of scattering by several strictly convex obstacles, with smooth boundary and satisfying a non eclipse condition. We show, in dimension 2 only, the existence of a spectral gap for the meromorphic continuation of the Laplace operator outside the obstacles. The proof of this result relies on a reduction to an open hyperbolic quantum map, achieved in [arXiv:1105.3128]. In fact, we obtain a spectral gap for this type of objects, which also has applications in potential scattering. The second main ingredient of this article is a fractal uncertainty principle. We adapt the techniques of [arXiv:1906.08923] to apply this fractal uncertainty principle in our context." @default.
- W4226110007 created "2022-05-05" @default.
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- W4226110007 date "2022-01-20" @default.
- W4226110007 modified "2023-09-27" @default.
- W4226110007 title "Spectral gap for obstacle scattering in dimension 2" @default.
- W4226110007 doi "https://doi.org/10.48550/arxiv.2201.08259" @default.
- W4226110007 hasPublicationYear "2022" @default.
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