A note on the spectrum of the Neumann Laplacian in periodic waveguides
  We study the Neumann Laplacian $-\Delta^N$ restricted to a periodic waveguide. In this situation its spectrum $\sigma(-\Delta^N)$ presents a band structure. Our goal and strategy is to get spectral information from an analysis of the asymptotic behavior of these bands provided that the waveguide is sufficiently thin. 
Alessandra A. Verri and Carlos R. Mamani
math-ph math.MP