Lieb-Thirring inequalities for geometrically induced bound states
  We prove new inequalities of the Lieb-Thirring type on the eigenvalues of Schr\"odinger operators in wave guides with local perturbations. The estimates are optimal in the weak-coupling case. To illustrate their applications, we consider, in particular, a straight strip and a straight circular tube with either mixed boundary conditions or boundary deformations. 
Pavel Exner, Helmut Linde and Timo Weidl