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  • Research Article
  • Open Access

Hardy inequalities in strips on ruled surfaces

Journal of Inequalities and Applications20062006:46409

  • Received: 17 August 2005
  • Accepted: 8 November 2005
  • Published:


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.


  • Gauss Curvature
  • Tubular Neighbourhood
  • Hardy Inequality
  • Ambient Surface
  • Negative Gauss Curvature


Authors’ Affiliations

Department of Theoretical Physics, Nuclear Physics Institute, Academy of Sciences of the Czech Republic, Řež, 250 68, Czech Republic


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© David Krejčiřík. 2006

This article is published under license to BioMed Central Ltd. 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.