Exponential Bounds on Curvature-Induced Resonances in a Two-Dimensional Dirichlet Tube
Abstract
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→0+
, provided the curvature of the strip axis satisfies certain analyticity and decay requirements.