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 P'.
|Original language||English (US)|
|Number of pages||4|
|Journal||Comptes Rendus Mathematique|
|State||Published - Apr 1 2016|
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