Extremal metrics for the -curvature in three dimensions

  • Jeffrey S. Case

    Penn State University, University Park, USA
  • Chin-Yu Hsiao

    Academia Sinica, Taipei, Taiwan
  • Paul Yang

    Princeton University, USA
Extremal metrics for the $Q^\prime$-curvature in three dimensions cover
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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