On Jang's equation and the Positive Mass Theorem for asymptotically hyperbolic initial data sets with dimensions above three and below eight

TL;DR

This paper proves the positive mass theorem for asymptotically hyperbolic initial data in dimensions 4 to 7 by solving Jang's equation, extending previous results beyond dimension three.

Contribution

It provides a non-spinor proof of the positive mass theorem in higher dimensions using solutions to Jang's equation in an asymptotically hyperbolic setting.

Findings

Established existence of solutions to Jang's equation in dimensions 4-7.

Provided a new proof of the positive mass theorem in these dimensions.

Extended previous results from dimension three to higher dimensions.

Abstract

We solve the Jang equation with respect to asymptotically hyperbolic "hyperboloidal" initial data in dimensions n = 4, 5, 6, 7. This gives a non-spinor proof of the positive mass theorem in the asymptotically hyperbolic setting in these dimensions. Our work extends an earlier result of [Sak21] obtained in dimension n = 3.