Spectral deformations and exponential decay of eigenfunctions for the Neumann Laplacian on manifolds with quasicylindrical ends

We study spectral properties of the Neumann Laplacian on manifolds with quasicylindrical ends. In particular, we prove exponential decay of the non-threshold eigenfunctions and show that the eigenvalues can accumulate only at thresholds of the absolutely continuous spectrum and only from below. The non-threshold eigenvalues are also discrete eigenvalues of a non-selfadjoint operator.