Inequalities and bounds for the eigenvalues of the sub-Laplacian on a strictly pseudoconvex CR manifold

We establish inequalities for the eigenvalues of the sub-Laplace operator associated with a pseudo-Hermitian structure on a strictly pseudoconvex CR manifold. Our inequalities extend those obtained by Niu and Zhang \cite{ NiuZhang} for the Dirichlet eigenvalues of the sub-Laplacian on a bounded domain in the Heisenberg group and are in the spirit of the well known Payne-P\'{ o}lya-Weinberger and Yang universal inequalities.

Categories: math.MG math.DG math.SP