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 $$3\le n \le 7$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>3</mml:mn> <mml:mo>≤</mml:mo> <mml:mi>n</mml:mi> <mml:mo>≤</mml:mo> <mml:mn>7</mml:mn> </mml:mrow> </mml:math> for a very general class of asymptotics. Potential applications to spacetime positive mass theorems for asymptotically anti-de Sitter initial data sets are discussed.