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Annales Henri Poincaré

, Volume 19, Issue 7, pp 2069–2086 | Cite as

Ruled Strips with Asymptotically Diverging Twisting

  • David KrejčiříkEmail author
  • Rafael Tiedra de Aldecoa
Article

Abstract

We consider the Dirichlet Laplacian in a two-dimensional strip composed of segments translated along a straight line with respect to a rotation angle with velocity diverging at infinity. We show that this model exhibits a “raise of dimension” at infinity leading to an essential spectrum determined by an asymptotic three-dimensional tube of annular cross section. If the cross section of the asymptotic tube is a disc, we also prove the existence of discrete eigenvalues below the essential spectrum.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics Faculty of Nuclear Sciences and Physical EngineeringCzech Technical University in PraguePrague 2Czech Republic
  2. 2.Facultad de MatemáticasPontificia Universidad Católica de ChileSantiago de ChileChile

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