BooksecrCollected Volumepp. 261–269

A lower bound to the spectral threshold in curved quantum layers

  • Pedro Freitas

    Universidade de Lisboa, Portugal
  • David Krejčiřík

    Czech Technical University in Prague, Prague, Czech Republic
A lower bound to the spectral threshold in curved quantum layers cover
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Abstract

We derive a lower bound to the spectral threshold of the Dirichlet Laplacian in tubular neighbourhoods of constant radius about complete surfaces. This lower bound is given by the lowest eigenvalue of a one-dimensional operator depending on the radius and principal curvatures of the reference surface. Moreover, we show that it is optimal if the reference surface is non-negatively curved.