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

David Lundberg

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arXiv · 2309.11330

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

David Lundberg

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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.

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David Lundberg. 2023-09-20. On Jang's equation and the Positive Mass Theorem for asymptotically hyperbolic initial data sets with dimensions above three and below eight. https://arxiv.org/abs/2309.11330

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