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

Princeton University

Research output: Contribution to journal › Article › peer-review

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.

Original language	American English
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 - 2019

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

Keywords

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

Access to Document

10.4171/JEMS/845

Cite this

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title = "Extremal metrics for the Q0-curvature in three dimensions",

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.",

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

author = "Case, \{Jeffrey S.\} and Hsiao, \{Chin Yu\} and Paul Yang",

note = "Publisher Copyright: {\textcopyright} European Mathematical Society 2019",

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AU - Case, Jeffrey S.

AU - Hsiao, Chin Yu

AU - Yang, Paul

N1 - Publisher Copyright: © European Mathematical Society 2019

PY - 2019

Y1 - 2019

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AB - 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.

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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DO - 10.4171/JEMS/845

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