Maximal hypersurfaces in asymptotically Anti-de Sitter spacetime

TL;DR

This paper establishes fundamental mathematical results—uniqueness, existence, and regularity—for maximal hypersurfaces in asymptotically Anti-de Sitter spacetimes, which are important in theoretical physics and geometric analysis.

Contribution

It provides the first comprehensive proof of these properties for maximal hypersurfaces in asymptotically AdS spacetimes with conformal boundary conditions.

Findings

Proved uniqueness of maximal hypersurfaces in the specified spacetime class.

Established existence of such hypersurfaces under given conditions.

Demonstrated regularity properties ensuring smoothness and well-behaved geometry.

Abstract

We prove uniqueness, existence, and regularity results for maximal hypersurfaces in spacetimes with a conformal completion at timelike infinity and asymptotically constant scalar curvature, as relevant for asymptotically AdS spacetimes. This work is dedicated to Yvonne Choquet-Bruhat on the occasion of her upcoming 99th birthday.