Journal of Inequalities and Applications
Volume 2006 (2006), Article ID 46409, 10 pages
Hardy inequalities in strips on ruled surfaces
Department of Theoretical Physics, Nuclear Physics Institute, Academy of Sciences of the Czech Republic, Řež 250 68, Czech Republic
Received 17 August 2005; Accepted 8 November 2005
Copyright © 2006 David Krejčiřík. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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 we use this to prove certain stability of spectrum in the case of asymptotically straight strips about mildly perturbed geodesics.