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  • Research Article
  • Open Access

Hardy inequalities in strips on ruled surfaces

Journal of Inequalities and Applications20062006:46409

https://doi.org/10.1155/JIA/2006/46409

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

Abstract

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.

Keywords

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

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Authors’ Affiliations

(1)
Department of Theoretical Physics, Nuclear Physics Institute, Academy of Sciences of the Czech Republic, Řež, 250 68, Czech Republic

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