Eigenvalues of the Kohn Laplacian and deformations of pseudohermitian structures on CR manifolds

We study the eigenvalues of the Kohn Laplacian on a closed embedded strictly pseudoconvex CR manifold as functionals on the set of positive oriented pseudohermitian struc-tures symbolscript We show that the functionals are continuous with respect to a natural topology on symbolscript Using an adaptation of the standard Kato-Rellich perturbation theory, we prove that the functionals are (one-sided) differentiable along 1-parameter analytic deformations. We use this differentiability to define the notion of critical pseudohermitian structures, in a general-ized sense, for them. We give a necessary (also sufficient in some situations) condition for a pseudohermitian structure to be critical. Finally, we present explicit examples of critical pseu-dohermitian structures on both homogeneous and non-homogeneous CR manifolds.