Extremal metrics for the Q0-curvature in three dimensions

Jeffrey S. Case; Chin Yu Hsiao; Paul Yang

doi:10.4171/JEMS/845

Extremal metrics for the Q⁰-curvature in three dimensions

Jeffrey S. Case, Chin Yu Hsiao, Paul Yang

Mathematics

Research output: Contribution to journal › Article

Abstract

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 language	English (US)
Pages (from-to)	585-626
Number of pages	42
Journal	Journal of the European Mathematical Society
Volume	21
Issue number	2
DOIs	https://doi.org/10.4171/JEMS/845
State	Published - Jan 1 2019

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

Keywords

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

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10.4171/JEMS/845

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Case, J. S., Hsiao, C. Y., & Yang, P. (2019). Extremal metrics for the Q⁰-curvature in three dimensions. Journal of the European Mathematical Society, 21(2), 585-626. https://doi.org/10.4171/JEMS/845

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