Hardy inequalities in strips on ruled surfaces

David Krejcirik

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Hardy inequalities in strips on ruled surfaces

David Krejcirik

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

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BibTeX RIS

David Krejcirik. 2005-11-10. Hardy inequalities in strips on ruled surfaces. https://arxiv.org/abs/math/0511257

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