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We estimate the ground state energy for the magnetic Laplacian with a Robincondition. In a special asymptotic limit, we find that the magnetic field doesnot contribute to the two-term expansion of the ground state energy, therebyproving that the Robin condition weakens diamagnetism. We discuss asemi-classical version of the operator and prove that the ground statesconcentrate near the boundary points of maximal curvature.

Diamagnetism versus Robin condition and concentration of ground states