Title: Resolvent estimates on asymptotically cylindrical manifolds and on the half line,
Abstract: Manifolds with infinite cylindrical ends have continuous spectrum of
increasing multiplicity as energy grows, and in general embedded resonances and
eigenvalues can accumulate at infinity. However, we prove that if geodesic
trapping is sufficiently mild, then such an accumulation is ruled out, and
moreover the cutoff resolvent is uniformly bounded at high energies. We obtain
as a corollary the existence of resonance free regions near the continuous
spectrum.
We also obtain improved estimates when the resolvent is cut off away from
part of the trapping, and along the way we prove some resolvent estimates for
repulsive potentials on the half line which may be of independent interest.