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 › peer-review

1 Scopus citations

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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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 ",

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

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AU - Hsiao, Chin Yu

AU - Yang, Paul

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N2 - 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

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KW - Beckner–Onofri inequality

KW - CR manifolds

KW - Green function asymptotics

KW - Pseudo-Einstein structures

KW - Pseudodifferential operator

KW - Q-prime curvature

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