## Duke Mathematical Journal

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

#### Abstract

Let $M^{3}$ 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 $M^{3}$ 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

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

Dates
First available in Project Euclid: 29 November 2012

https://projecteuclid.org/euclid.dmj/1354198149

Digital Object Identifier
doi:10.1215/00127094-1902154

Mathematical Reviews number (MathSciNet)
MR2999315

Zentralblatt MATH identifier
1271.32040

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

#### Citation

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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