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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 that 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’s function for root P ‘. (C) 2015 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.
Publication Date: Apr-2016
Electronic Publication Date: 8-Feb-2016
Citation: Case, Jeffrey S, Hsiao, Chin-Yu, Yang, Paul. (2016). Extremal metrics for the Q ‘-curvature in three dimensions. COMPTES RENDUS MATHEMATIQUE, 354 (407 - 410. doi:10.1016/j.crma.2015.12.012
DOI: doi:10.1016/j.crma.2015.12.012
ISSN: 1631-073X
EISSN: 1778-3569
Pages: 407 - 410
Language: English
Type of Material: Journal Article
Version: Author's manuscript

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