Inequalities between Dirichlet and Neumann Eigenvalues on the Heisenberg Group

@inproceedings{Frank2008InequalitiesBD,
  title={Inequalities between Dirichlet and Neumann Eigenvalues on the Heisenberg Group},
  author={Rupert L. Frank and Ari Laptev},
  year={2008}
}
We prove that for any domain in the Heisenberg group the k + 1 st Neumann eigenvalue of the sub-Laplacian is strictly less than the k th Dirichlet eigenvalue. As a byproduct we obtain similar inequalities for the Euclidean Laplacian with a homogeneous magnetic field. 
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