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We prove that for any domain in the Heisenberg group the (k+1)'th Neumanneigenvalue of the sub-Laplacian is strictly less than the k'th Dirichleteigenvalue. As a byproduct we obtain similar inequalities for the EuclideanLaplacian with a homogeneous magnetic field.

Inequalities between Dirichlet and Neumann eigenvalues on the Heisenberg group