Extremal metrics for the Q0-curvature in three dimensions

Jeffrey S. Case, Chin Yu Hsiao, Paul Yang

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We construct contact forms with constant Q0-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 P0-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 P0

Original languageEnglish (US)
Pages (from-to)585-626
Number of pages42
JournalJournal of the European Mathematical Society
Issue number2
StatePublished - 2019

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics


  • Beckner–Onofri inequality
  • CR manifolds
  • Green function asymptotics
  • Pseudo-Einstein structures
  • Pseudodifferential operator
  • Q-prime curvature


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