Seminario Fismat | Resonances in deformed tubes: twisting and bending

Pablo Miranda (Universidad de Santiago de Chile)

In this talk we will consider an infinite straight tube and we will deform it by a periodic twisting and a local bending. On the deformed tube we will define the Laplacian and will study the existence of scattering resonances created by the deformations. We will show the existence of exactly one resonance or one eigenvalue near the bottom of the essential spectrum, depending on the strength of the twisting and the bending. We will also obtain the asymptotic behavior of the resonance/eigenvalue as a function of the bending and twisting.