Pseudo-Einstein and Q-flat metrics with eigenvalue estimates on CR-hypersurfaces

Abstract

Let $M^{2n-1}$ be the smooth boundary of a bounded strongly pseudo-convex domain $\Omega$ in a complete Stein manifold $V^{2n}$. Then (1) For $n\ge 3$, $M^{2n-1}$ admits a pseudo-Eistein metric; (2) For $n\ge 2$, $M^{2n-1}$ admits a Fefferman metric of zero CR Q-curvature; and (3) for a compact strictly pseudoconvex CR embeddable 3-manifold $M^3$, its CR Paneitz operator $P$ is a closed operator.