Hardy inequalities in strips on ruled surfaces
Spectral Theory
2007-05-23 v1 Mathematical Physics
Differential Geometry
math.MP
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.
Cite
@article{arxiv.math/0511257,
title = {Hardy inequalities in strips on ruled surfaces},
author = {David Krejcirik},
journal= {arXiv preprint arXiv:math/0511257},
year = {2007}
}
Comments
LaTeX, 10 pages; to appear in Journal of Inequalities and Applications