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Scattering resonances on
truncated cones
Dean Baskin and Mengxuan Yang |
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Vol. 2 (2020), No. 2, 385–396
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Abstract |
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We consider the problem of finding the resonances of the Laplacian on truncated Riemannian cones. In a similar fashion to Cheeger and 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 , where is an explicit coefficient. We also conclude that the Laplacian on a nontruncated cone has no resonances. |
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Keywords
resonances, cones
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Mathematical Subject Classification 2010
Primary: 33C10, 35L05, 58J50
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Milestones
Received: 23 April 2019
Revised: 30 September 2019
Accepted: 19 November 2019
Published: 22 May 2020
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Authors |
| Dean Baskin | |
| Department of Mathematics Texas A&M University College Station, TX United States |
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| Mengxuan Yang | |
| Department of Mathematics Northwestern University Evanston, IL United States |
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