Scattering resonances on truncated cones
Analysis of PDEs
2020-05-27 v3 Spectral Theory
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.
Keywords
Cite
@article{arxiv.1903.02654,
title = {Scattering resonances on truncated cones},
author = {Dean Baskin and Mengxuan Yang},
journal= {arXiv preprint arXiv:1903.02654},
year = {2020}
}
Comments
11 pages. Version 2: updated to reflect subtlety at zero. Version 3: minor revisions for clarity in response to anonymous referee