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

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).