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

2023/09/20 by David Lundberg, Lundberg, David
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2309.11330

openalex publication_date 2023/09/20 · openalex created_date 2023/09/22 · openalex updated_date 2026/07/28

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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