Open Access

Hardy inequalities in strips on ruled surfaces

Journal of Inequalities and Applications20062006:46409

DOI: 10.1155/JIA/2006/46409

Received: 17 August 2005

Accepted: 8 November 2005

Published: 17 May 2006

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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Authors’ Affiliations

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

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Copyright

© 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.