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arXiv · 1511.05013

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

Jeffrey S. Case·Chin-Yu Hsiao·Paul Yang
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Abstract

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's function for $\sqrt{P^\prime}$.

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Jeffrey S. Case, Chin-Yu Hsiao, Paul Yang. 2015-11-16. Extremal metrics for the $Q^\prime$-curvature in three dimensions. https://arxiv.org/abs/1511.05013

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