Vol. 2, No. 2, 2020

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Scattering resonances on truncated cones

Dean Baskin and Mengxuan Yang

Vol. 2 (2020), No. 2, 385–396
Abstract

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 Arn + o(rn), where A is an explicit coefficient. We also conclude that the Laplacian on a nontruncated cone has no resonances.

Keywords
resonances, cones
Mathematical Subject Classification 2010
Primary: 33C10, 35L05, 58J50
Milestones
Received: 23 April 2019
Revised: 30 September 2019
Accepted: 19 November 2019
Published: 22 May 2020
Authors
Dean Baskin
Department of Mathematics
Texas A&M University
College Station, TX
United States
Mengxuan Yang
Department of Mathematics
Northwestern University
Evanston, IL
United States