Embeddability for 3-dimensional Cauchy-Riemann manifolds and cryamabe invariants

Sagun Chanillo, Hung Lin Chiu, Paul Yang

Research output: Contribution to journalArticle

23 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)2909-2921
Number of pages13
JournalDuke Mathematical Journal
Volume161
Issue number15
DOIs
StatePublished - Dec 1 2012

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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