Exponential Bounds on Curvature-Induced Resonances in a Two-Dimensional Dirichlet Tube

We consider curvature-induced resonances in a planar two-dimensional Dirichlet tube of a width $ d $. It is shown that the distances of the corresponding resonance poles from the real axis are exponentially small as $ d\to 0+ $, provided the curvature of the strip axis satisfies certain analyticity and decay requirements.