English

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

Differential Geometry 2023-09-21 v1 General Relativity and Quantum Cosmology Analysis of PDEs

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.

Keywords

Cite

@article{arxiv.2309.11330,
  title  = {On Jang's equation and the Positive Mass Theorem for asymptotically hyperbolic initial data sets with dimensions above three and below eight},
  author = {David Lundberg},
  journal= {arXiv preprint arXiv:2309.11330},
  year   = {2023}
}

Comments

Thesis version of 110 pages. Comments welcome!