  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.

Differential Geometry;General Relativity and Quantum Cosmology;Analysis of PDEs