David Krejcirik
Published 2007-12-20, updated 2009-03-25Version 2
We make an overview of spectral-geometric effects of twisting and bending in quantum waveguides modelled by the Dirichlet Laplacian in an unbounded three-dimensional tube of uniform cross-section. We focus on the existence of Hardy-type inequalities in twisted tubes of non-circular cross-section.
Comments: 20 pages, LaTeX with 3 EPS figures. This is a corrected version of the published paper; errata in Section 6 corrected
Journal: Proc. Sympos. Pure Math., vol. 77, pp. 617-636, Amer. Math. Soc., Providence, RI, 2008
Spectrum of Dirichlet Laplacian in a conical layer
Lower bounds for Dirichlet Laplacians and uncertainty principles
Spectral estimates for Dirichlet Laplacians on perturbed twisted tubes
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