Geodesic
Gap opening around a given point of the spectrum of a cylindrical waveguide by means of gentle periodic perturbation of walls
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 43, Tome 422 (2014), pp. 90-130 Cet article a éte moissonné depuis la source Math-Net.Ru

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We discuss one of the main questions in band-gap engineering, namely by an asymptotic analysis it is proven that any given point of a certain interval in the spectrum of a cylindrical waveguide can be surrounded with a spectral gap by means of a periodical perturbation of the walls. Both the Dirichlet and Neumann boundary conditions for the Laplace operator are considered in planar and multi-dimensional waveguides. 
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S. A. Nazarov. Gap opening around a given point of the spectrum of a cylindrical waveguide by means of gentle periodic perturbation of walls. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 43, Tome 422 (2014), pp. 90-130. http://geodesic.mathdoc.fr/item/ZNSL_2014_422_a5/

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