Existence and Uniqueness of constant mean curvature foliation of asymptotically hyperbolic 3-manifolds II

TL;DR

This paper extends the existence and uniqueness of constant mean curvature foliations to a broader class of asymptotically hyperbolic 3-manifolds with positive mass trace, using advanced geometric analysis techniques.

Contribution

It generalizes previous results by including all asymptotically hyperbolic metrics with positive mass trace, combining Kazdan-Warner obstructions with De Lellis and Müller's theorem.

Findings

Established existence of CMC foliation for wider class of metrics.

Proved uniqueness of the foliation under new conditions.

Extended previous asymptotic analysis to all positive mass trace cases.

Abstract

In a previous paper, the authors showed that metrics which are asymptotic to Anti-de Sitter-Schwarzschild metrics with positive mass admit a unique foliation by stable spheres with constant mean curvature. In this paper we extend that result to all asymptotically hyperbolic metrics for which the trace of the mass term is positive. We do this by combining the Kazdan-Warner obstructions with a theorem due to De Lellis and M\"uller.