Nonnegativity of the CR Paneitz operator for embeddable CR manifolds

Abstract

The nonnegativity of the CR Paneitz operator plays a crucial role in three-dimensional CR geometry. In this paper, we prove this nonnegativity for embeddable CR manifolds. This result and previous works give an affirmative solution of the CR Yamabe problem for embeddable CR manifolds. We also show the existence of a contact form with zero CR $Q$-curvature, and generalize the total $Q$-prime curvature to embeddable CR manifolds with no pseudo-Einstein contact forms. Furthermore, we discuss the logarithmic singularity of the Szegő kernel.

arXiv comment16 pages, revised version

References in corpus (4)

• Ambient metric construction of Q-curvature in conformal and CR geometries
• Embeddability for Three-Dimensional Cauchy-Riemann Manifolds and CR Yamabe Invariants
• Q-prime curvature on CR manifolds
• Ambient constructions for Sasakian $\eta$-Einstein manifolds

Cited by in corpus (6)

• An upper bound for the first positive eigenvalue of the Kohn Laplacian on Reinhardt real hypersurfaces
• CR $Q$-curvature and CR pluriharmonic functions
• Analysis of the critical CR GJMS operator
• Deformations and embeddings of three-dimensional strictly pseudoconvex CR manifolds
• Positive mass theorem and the Yamabe equation on CR manifolds
• CR Yamabe constant and inequivalent CR structures