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An integral formula for the $ Q$-prime curvature in 3-dimensional CR geometry


Authors: Jeffrey S. Case, Jih-Hsin Cheng and Paul Yang
Journal: Proc. Amer. Math. Soc. 147 (2019), 1577-1586
MSC (2010): Primary 32V05; Secondary 32V20
DOI: https://doi.org/10.1090/proc/14328
Published electronically: December 6, 2018
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Abstract: We give an integral formula for the total $ Q^\prime $-curvature of a three-dimensional CR manifold with positive CR Yamabe constant and nonnegative Paneitz operator. Our derivation includes a relationship between the Green's functions of the CR Laplacian and the $ P^\prime $-operator.


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Additional Information

Jeffrey S. Case
Affiliation: Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802
Email: jqc5026@psu.edu

Jih-Hsin Cheng
Affiliation: Institute of Mathematics, Academia Sinica, Taipei and National Center for Theoretical Sciences, Taipei Office, Taiwan, Republic of China
Email: cheng@math.sinica.edu.tw

Paul Yang
Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
Email: yang@math.princeton.edu

DOI: https://doi.org/10.1090/proc/14328
Received by editor(s): September 15, 2017
Received by editor(s) in revised form: July 19, 2018
Published electronically: December 6, 2018
Additional Notes: The first author was supported by a grant from the Simons Foundation (Grant No. 524601).
The second author would like to thank the Ministry of Science and Technology of Taiwan, R.O.C., for support of the project via MOST 106-2115-M-001-013 and the National Center for Theoretical Sciences for the constant support.
The third author was supported by NSF grant DMS-1509505.
Communicated by: Jia-Ping Wang
Article copyright: © Copyright 2018 American Mathematical Society