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Hardy inequalities in strips on ruled surfaces

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.

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Correspondence to David Krejčiřík.

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Krejčiřík, D. Hardy inequalities in strips on ruled surfaces. J Inequal Appl 2006, 46409 (2006). https://doi.org/10.1155/JIA/2006/46409

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Keywords

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