Extremal metrics for the Q'-curvature in three dimensions

Jeffrey Steven Case, Chin Yu Hsiao, Paul Yang

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We construct contact forms with constant Q'-curvature on compact three-dimensional CR manifolds that 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'-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 P'.

Original languageEnglish (US)
Pages (from-to)407-410
Number of pages4
JournalComptes Rendus Mathematique
Volume354
Issue number4
DOIs
StatePublished - Apr 1 2016

Fingerprint

Q-curvature
Contact Form
Three-dimension
Metric
Conformal Geometry
CR Manifold
Pseudodifferential Operators
Elliptic Operator
Positivity
Albert Einstein
Asymptotic Expansion
Green's function
Analogue
Three-dimensional
Term
Operator

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Case, Jeffrey Steven ; Hsiao, Chin Yu ; Yang, Paul. / Extremal metrics for the Q'-curvature in three dimensions. In: Comptes Rendus Mathematique. 2016 ; Vol. 354, No. 4. pp. 407-410.
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Extremal metrics for the Q'-curvature in three dimensions. / Case, Jeffrey Steven; Hsiao, Chin Yu; Yang, Paul.

In: Comptes Rendus Mathematique, Vol. 354, No. 4, 01.04.2016, p. 407-410.

Research output: Contribution to journalArticle

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