Abstract
In this paper, we will use the Kohn's ∂ b -theory on CR-hypersurfaces to derive some new results in CR-geometry. Main Theorem. Let M 2n-1 be the smooth boundary of a bounded strongly pseudo-convex domain Ω in a complete Stein manifold V 2n . Then: (1) For n ≥ 3, M 2n-1 admits a pseudo-Einstein metric. (2) For n > 2, M 2n-1 admits a Fefferman metric of zero CR Q-curvature. (3) In addition, for a compact strictly pseudoconvex CR emendable 3-manifold M 3 , its CR Paneitz operator P is a closed operator. There are examples of non-emendable strongly pseudoconvex CR-manifolds M 3 , for which the corresponding ∂ b -operator and Paneitz operators are not closed operators.
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