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The Jang Equation Reduction of the Spacetime Positive Energy Theorem in Dimensions Less Than Eight

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Abstract

We extend the Jang equation proof of the positive energy theorem due to Schoen and Yau (Commun Math Phys 79(2):231–260, 1981) from dimension n =  3 to dimensions 3 ≤  n < 8. This requires us to address several technical difficulties that are not present when n =  3. The regularity and decay assumptions for the initial data sets to which our argument applies are weaker than those in Schoen and Yau (Commun Math Phys 79(2):231–260, 1981).

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Authors and Affiliations

  1. Departement Mathematik, ETH Zürich, 8092, Zürich, Switzerland

    Michael Eichmair

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  1. Michael Eichmair
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Correspondence to Michael Eichmair.

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Communicated by P. T. Chruściel

The author gratefully acknowledges the support of NSF grant DMS-0906038 and of SNF grant 2-77348-12.

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Eichmair, M. The Jang Equation Reduction of the Spacetime Positive Energy Theorem in Dimensions Less Than Eight. Commun. Math. Phys. 319, 575–593 (2013). https://doi.org/10.1007/s00220-013-1700-7

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