
Resumo: Let −∆DΩ be the Dirichlet Laplacian in a three dimensional waveguide Ω. If Ω is bounded, it is known that the spectrum of −∆DΩ is purely discrete. The situation changes when Ω is unbounded. For example, if Ω is a straight infinite waveguide, the operator −∆DΩ does not have discrete eigenvalues. However, local deformations in Ω can create them. In this talk some constructions for Ω will be presented to show how its geometry can affect the spectral behavior of −∆DΩ . In particular, when Ω is a broken sheared waveguide, we will show that the discrete spectrum is non empty.
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