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EMBEDDABILITY FOR 3-DIMENSIONAL CAUCHY-RIEMANN MANIFOLDS AND CR YAMABE INVARIANTS

Author(s): Chanillo, Sagun; Chiu, Hung-Lin; Yang, Paul C.

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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.
Publication Date: 1-Dec-2012
Electronic Publication Date: 29-Nov-2012
Citation: Chanillo, Sagun, Chiu, Hung-Lin, Yang, Paul. (2012). EMBEDDABILITY FOR 3-DIMENSIONAL CAUCHY-RIEMANN MANIFOLDS AND CR YAMABE INVARIANTS. DUKE MATHEMATICAL JOURNAL, 161 (2909 - 2921). doi:10.1215/00127094-1902154
DOI: doi:10.1215/00127094-1902154
ISSN: 0012-7094
Pages: 2909 - 2921
Language: English
Type of Material: Journal Article
Journal/Proceeding Title: DUKE MATHEMATICAL JOURNAL
Version: Author's manuscript



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