A lower bound to the spectral threshold in curved quantum layers
Mathematical Physics
2017-09-08 v1 Differential Geometry
math.MP
Spectral Theory
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.
Keywords
Cite
@article{arxiv.1602.04990,
title = {A lower bound to the spectral threshold in curved quantum layers},
author = {Pedro Freitas and David Krejcirik},
journal= {arXiv preprint arXiv:1602.04990},
year = {2017}
}
Comments
Dedicated to Pavel Exner on the occasion of his 70th birthday