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Quasi-Local Mass Integrals and the Total Mass

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Abstract

On asymptotically flat and asymptotically hyperbolic manifolds, by evaluating the total mass via the Ricci tensor, we show that the limits of certain Brown–York type and Hawking type quasi-local mass integrals equal the total mass of the manifold in all dimensions.

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Authors and Affiliations

  1. Department of Mathematics, University of Miami, Coral Gables, FL, 33146, USA

    Pengzi Miao

  2. The Institute of Mathematical Sciences and Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong, China

    Luen-Fai Tam

  3. School of Mathematical Sciences, Fudan University, Shanghai, 200433, China

    Naqing **e

Authors
  1. Pengzi Miao
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  2. Luen-Fai Tam
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  3. Naqing **e
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Corresponding author

Correspondence to Luen-Fai Tam.

Additional information

Pengzi Miao: Research partially supported by Simons Foundation Collaboration Grant for Mathematicians #281105. Luen-Fai Tam: Research partially supported by Hong Kong RGC General Research Fund #CUHK 14305114. Naqing **e: Research partially supported by the National Science Foundation of China #11421061.

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Miao, P., Tam, LF. & **e, N. Quasi-Local Mass Integrals and the Total Mass. J Geom Anal 27, 1323–1354 (2017). https://doi.org/10.1007/s12220-016-9721-z

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  • DOI: https://doi.org/10.1007/s12220-016-9721-z

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