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

TL;DR

This paper rigorously analyzes the generalized Jang equation in asymptotically anti-de Sitter spaces, exploring solution existence and properties, with implications for positive mass theorems in higher-dimensional spacetimes.

Contribution

It provides a comprehensive mathematical analysis of the generalized Jang equation in a broad asymptotic setting, extending previous work to higher dimensions and general asymptotics.

Findings

Existence and properties of solutions established for 3 to 7 dimensions.

Potential applications to positive mass theorems in asymptotically anti-de Sitter spacetimes.

Framework applicable to a wide class of asymptotic conditions.

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 $3\leq n \leq 7$ for a very general class of asymptotics. Potential applications to spacetime positive mass theorems for asymptotically anti-de Sitter initial data sets are discussed.