Extremal metrics for the ${Q}^\prime$-curvature in three dimensions

Chin-Yu Hsiao Institute of Mathematics, Academia Sinica, Taiwan Jeffrey Case Department of Mathematics, The Pennsylvania State University Paul Yang Department of Mathematics, Princeton University

Differential Geometry mathscidoc:1803.10003

We construct contact forms with constant $Q^\prime$-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 $P^\prime$-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 $\sqrt{P^\prime}$.
CR geometry, ${Q}^\prime$-curvature in CR geometry
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  • to appear in Journal of the European Mathematical Society
  title={Extremal metrics for the ${Q}^\prime$-curvature in three dimensions},
  author={Chin-Yu Hsiao, Jeffrey Case, and Paul Yang},
Chin-Yu Hsiao, Jeffrey Case, and Paul Yang. Extremal metrics for the ${Q}^\prime$-curvature in three dimensions. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180330000824722601002.
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