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1 December 2020 Nonnegativity of the CR Paneitz operator for embeddable CR manifolds
Yuya Takeuchi
Duke Math. J. 169(18): 3417-3438 (1 December 2020). DOI: 10.1215/00127094-2020-0051

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 gives an affirmative solution to 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.

Citation

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Yuya Takeuchi. "Nonnegativity of the CR Paneitz operator for embeddable CR manifolds." Duke Math. J. 169 (18) 3417 - 3438, 1 December 2020. https://doi.org/10.1215/00127094-2020-0051

Information

Received: 1 November 2019; Revised: 15 March 2020; Published: 1 December 2020
First available in Project Euclid: 1 December 2020

MathSciNet: MR4181029
Digital Object Identifier: 10.1215/00127094-2020-0051

Subjects:
Primary: 32V20
Secondary: 32V15, 32V30, 53C55

Rights: Copyright © 2020 Duke University Press

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Vol.169 • No. 18 • 1 December 2020
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