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Universal Positive Mass Theorems

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Abstract

In this paper, we develop a general study of contributions at infinity of Bochner–Weitzenböck-type formulas on asymptotically flat manifolds, inspired by Witten’s proof of the positive mass theorem. As an application, we show that similar proofs can be obtained in a much more general setting as any choice of an irreducible natural bundle and a very large choice of first-order operators may lead to a positive mass theorem along the same lines if the necessary curvature conditions are satisfied.

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Authors and Affiliations

  1. Institut Montpelliérain Alexander Grothendieck, Université de Montpellier, UMR 5149 CNRS, Montpellier, France

    Marc Herzlich

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  1. Marc Herzlich
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Correspondence to Marc Herzlich.

Additional information

Communicated by P. T. Chruściel

The author is supported in part by the project ANR-12-BS01-004 ‘Geometry and topology of open manifolds’ of the French National Agency for Research.

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Herzlich, M. Universal Positive Mass Theorems. Commun. Math. Phys. 351, 973–992 (2017). https://doi.org/10.1007/s00220-016-2777-6

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  • DOI: https://doi.org/10.1007/s00220-016-2777-6

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