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

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