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

2006/09/11 by Jianguo Cao, Cao, Jianguo, Shu-Cheng Chang +1
Mathematics · #32V15 #53C56 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #math.CV #math.DG #msc:32V15 #msc:53C56

paper · pdf · doi:10.48550/arxiv.math/0609312

arxiv created 2007/10/15 · arxiv updated 2009/12/01

Abstract

Let M^2n-1 be the smooth boundary of a bounded strongly pseudo-convex domain Ω in a complete Stein manifold V²ⁿ. Then (1) For n ≥ 3, M^2n-1 admits a pseudo-Eistein metric; (2) For n ≥ 2, M^2n-1 admits a Fefferman metric of zero CR Q-curvature; and (3) for a compact strictly pseudoconvex CR embeddable 3-manifold M³, its CR Paneitz operator P is a closed operator.

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