Paper detail

On resonances generated by conic diffraction

We describe the resonances closest to the real axis generated by diffraction of waves among cone points on a manifold with Euclidean ends. These resonances lie asymptotically evenly spaced along a curve of the form $$\frac{\Im λ}{\log \left |\Re λ\right |}= -ν;$$ here $ν=(n-1)/2 L_0$ where $n$ is the dimension and $L_0$ is the length of the longest geodesic connecting two cone points. Moreover there are asymptotically no resonances below this curve and above the curve $$ \frac{\Im λ}{\log \left |\Re λ\right |}= -Λ$$ for a fixed $Λ>ν.$