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Eigenvalues of the Kohn Laplacian and deformations of pseudohermitian structures on compact embedded strictly pseudoconvex CR manifolds. (arXiv:1901.05881v1 [math.CV])
来源于:arXiv
We study the eigenvalues of the Kohn Laplacian on a closed embedded strictly
pseudoconvex CR manifold as functionals on the set of positive oriented contact
forms $\mathcal{P}_+$. We show that the functionals are continuous with respect
to a natural topology on $\mathcal{P}_+$. Using a simple 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 contact forms, in a
generalized sense, for the functionals. We give a necessary (also sufficient in
some situations) condition for a contact form to be critical. Finally, we
present explicit examples of critical contact form on both homogeneous and
non-homogeneous CR manifolds. 查看全文>>