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Extremal metrics for the Q ‘-curvature in three dimensions

Author(s): Case, Jeffrey S; Hsiao, Chin-Yu; Yang, Paul C

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Abstract: We construct contact forms with constant Q’-curvature on compact three-dimensional CR manifolds which admit a pseudo-Einstein contact form and satisfy some natural positivity conditions. These contact forms are obtained by minimizing the CR analogue of the II-functional from conformal geometry. Two crucial steps are to show that the P’-operator can be regarded as an elliptic pseudodifferential operator and to compute the leading order terms of the asymptotic expansion of the Green function for root P’.
Publication Date: 2019
Electronic Publication Date: 9-Nov-2018
Citation: Case, Jeffrey S, Hsiao, Chin-Yu, Yang, Paul. (2019). Extremal metrics for the Q ‘-curvature in three dimensions. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 21 (585 - 626. doi:10.4171/JEMS/845
DOI: doi:10.4171/JEMS/845
ISSN: 1435-9855
Pages: 585 - 626
Language: English
Type of Material: Journal Article
Version: Author's manuscript

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