Journal
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY
Volume 21, Issue 2, Pages 585-626Publisher
EUROPEAN MATHEMATICAL SOC
DOI: 10.4171/JEMS/845
Keywords
Q-prime curvature; pseudo-Einstein structures; CR manifolds; pseudodifferential operator; Green function asymptotics; Beckner-Onofri inequality
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Funding
- Academia Sinica in Taipei
- Princeton University
- NSF [DMS-1004394, DMS-1509505]
- Simons Foundation [524601]
- Taiwan Ministry of Science of Technology [103-2115-M-001-001, 104-2628-M-001-003-MY2]
- Golden-Jade fellowship of Kenda Foundation
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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'.
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