Duke Mathematical Journal

Embeddability for 3-dimensional Cauchy–Riemann manifolds and CR Yamabe invariants

Sagun Chanillo, Hung-Lin Chiu, and Paul Yang

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Let M3 be a closed Cauchy–Riemann (CR) 3-manifold. In this article, we derive a Bochner formula for the Kohn Laplacian in which the pseudo-Hermitian torsion does not play any role. By means of this formula we show that the nonzero eigenvalues of the Kohn Laplacian have a positive lower bound, provided that the CR Paneitz operator is nonnegative and the Webster curvature is positive. This means that M3 is embeddable when the CR Yamabe constant is positive and the CR Paneitz operator is nonnegative. Our lower bound estimate is sharp. In addition, we show that the embedding is stable in the sense of Burns and Epstein.

Article information

Duke Math. J., Volume 161, Number 15 (2012), 2909-2921.

First available in Project Euclid: 29 November 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 32V30: Embeddings of CR manifolds
Secondary: 32V20: Analysis on CR manifolds


Chanillo, Sagun; Chiu, Hung-Lin; Yang, Paul. Embeddability for 3-dimensional Cauchy–Riemann manifolds and CR Yamabe invariants. Duke Math. J. 161 (2012), no. 15, 2909--2921. doi:10.1215/00127094-1902154. https://projecteuclid.org/euclid.dmj/1354198149

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