On the existence and properties of solutions of the generalized Jang equation with respect to asymptotically anti-de Sitter initial data

Abstract

We provide a rigorous analysis of the generalized Jang equation in the asymptotically anti-de Sitter setting modelled on constant time slices of anti-de Sitter spacetimes in dimensions $3\le n\le 7$ for a very general class of asymptotics. Potential applications to spacetime positive mass theorems for asymptotically anti-de Sitter initial data sets are discussed.

43 pages