Extremal metrics for the -curvature in three dimensions
Jeffrey S. Case
Penn State University, University Park, USAChin-Yu Hsiao
Academia Sinica, Taipei, TaiwanPaul Yang
Princeton University, USA
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Abstract
We construct contact forms with constant -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 -functional from conformal geometry. Two crucial steps are to show that the -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 .
Cite this article
Jeffrey S. Case, Chin-Yu Hsiao, Paul Yang, Extremal metrics for the -curvature in three dimensions. J. Eur. Math. Soc. 21 (2019), no. 2, pp. 585–626
DOI 10.4171/JEMS/845