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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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An integral formula for the $Q$-prime curvature in 3-dimensional CR geometry
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by Jeffrey S. Case, Jih-Hsin Cheng and Paul Yang PDF
Proc. Amer. Math. Soc. 147 (2019), 1577-1586 Request permission


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
  • MR Author ID: 894837
  • Email:
  • Jih-Hsin Cheng
  • Affiliation: Institute of Mathematics, Academia Sinica, Taipei and National Center for Theoretical Sciences, Taipei Office, Taiwan, Republic of China
  • MR Author ID: 247753
  • Email:
  • Paul Yang
  • Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
  • MR Author ID: 185315
  • Email:
  • 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
  • © Copyright 2018 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 147 (2019), 1577-1586
  • MSC (2010): Primary 32V05; Secondary 32V20
  • DOI:
  • MathSciNet review: 3910422