Hardy inequalities in strips on ruled surfaces
  We consider the Dirichlet Laplacian in infinite two-dimensional strips defined as uniform tubular neighbourhoods of curves on ruled surfaces. We show that the negative Gauss curvature of the ambient surface gives rise to a Hardy inequality and use this to prove certain stability of spectrum in the case of asymptotically straight strips about mildly perturbed geodesics. 
David Krejcirik