Hardy inequalities in strips on ruled surfaces

Details Hardy inequalities in strips on ruled surfaces Hardy inequalities in strips on ruled surfaces

2005-11-10

arxiv.org/abs/math/0511257v1

J. Inequal. Appl. 2006 (2006), Article ID 46409, 10 pages.

Mathematics

Spectral Theory

LaTeX, 10 pages; to appear in Journal of Inequalities and Applications

Scientific paper

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 use this to prove certain stability of spectrum in the case of
asymptotically straight strips about mildly perturbed geodesics.

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