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arXiv · 1903.02654

Scattering resonances on truncated cones

Dean Baskin·Mengxuan Yang
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Abstract

We consider the problem of finding the resonances of the Laplacian on truncated Riemannian cones. In a similar fashion to Cheeger--Taylor, we construct the resolvent and scattering matrix for the Laplacian on cones and truncated cones. Following Stefanov, we show that the resonances on the truncated cone are distributed asymptotically as Ar^n + o(r^n), where A is an explicit coefficient. We also conclude that the Laplacian on a non-truncated cone has no resonances away from zero.

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Dean Baskin, Mengxuan Yang. 2019-03-06. Scattering resonances on truncated cones. https://doi.org/10.2140/paa.2020.2.385

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