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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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Evaluation of the ADM mass and center of mass via the Ricci tensor
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by Pengzi Miao and Luen-Fai Tam PDF
Proc. Amer. Math. Soc. 144 (2016), 753-761 Request permission


We prove directly without using a density theorem that (i) the ADM mass defined in the usual way on an asymptotically flat manifold is equal to the mass defined intrinsically using the Ricci tensor; (ii) the Hamiltonian formulation of center of mass and the center of mass defined intrinsically using the Ricci tensor are the same.
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Additional Information
  • Pengzi Miao
  • Affiliation: Department of Mathematics, University of Miami, Coral Gables, Florida 33146
  • MR Author ID: 715810
  • Email:
  • Luen-Fai Tam
  • Affiliation: The Institute of Mathematical Sciences and Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong, People’s Republic of China
  • MR Author ID: 170445
  • Email:
  • Received by editor(s): August 26, 2014
  • Received by editor(s) in revised form: January 16, 2015
  • Published electronically: October 6, 2015
  • Additional Notes: The first author’s research was partially supported by Simons Foundation Collaboration Grant for Mathematicians #281105.
    The second author’s research was partially supported by Hong Kong RGC General Research Fund #CUHK 403108
  • Communicated by: Lei Ni
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 144 (2016), 753-761
  • MSC (2010): Primary 83C99; Secondary 53C20
  • DOI:
  • MathSciNet review: 3430851