Title: Resonances near Thresholds in slightly Twisted Waveguides,
Abstract: We consider the Dirichlet Laplacian in a straight three dimensional waveguide
with non-rotationally invariant cross section, perturbed by a twisting of small
amplitude. It is well known that such a perturbation does not create
eigenvalues below the essential spectrum. However, around the bottom of the
spectrum, we provide a meromorphic extension of the weighted resolvent of the
perturbed operator, and show the existence of exactly one resonance near this
point. Moreover, we obtain the asymptotic behavior of this resonance as the
size of the twisting goes to 0. We also extend the analysis to the upper
eigenvalues of the transversal problem, showing that the number of resonances
is bounded by the multiplicity of the eigenvalue and obtaining the
corresponding asymptotic behavior