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 Im λ log |Re λ| ⁼ −ν; here ν = (n − 1)/2L₀ where n is the dimension and L₀ is the length of the longest geodesic connecting two cone points. Moreover there are asymptotically no resonances below this curve and above the curve Im λ log |Re λ| ^{= −Λ} for a fixed Λ > ν.