Stability of the magnetic Schrodinger operator in a waveguide

The spectrum of the Schrodinger operator in a quantum waveguide is known to be unstable in two and three dimensions. Any local enlargement of the waveguide produces eigenvalues beneath the continuous spectrum. Also, if the waveguide is bent, eigenvalues will arise below the continuous spectrum. In this paper a magnetic field is added into the system. The spectrum of the magnetic Schrodinger operator is proved to be stable under small local deformations and also under small bending of the waveguide. The proof includes a magnetic Hardy-type inequality in the waveguide, which is interesting in its own right.