A compactly supported magnetic field renders the spectrum of the Dirichlet Laplacian on a waveguide stable under small boundary deformations.
Simon, The Bound State of Weakly Coupled Schr ¨odinger Operators in One and Two Dimensions, Ann
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Magnetic Dirichlet Laplacian on deformed waveguides
A compactly supported magnetic field renders the spectrum of the Dirichlet Laplacian on a waveguide stable under small boundary deformations.