There are a number of interesting inequalities satisfied by minimal-area surfaces in asymptotically hyperbolic geometries. In the static version of AdS/CFT, these surfaces are interpreted as the entropy of the corresponding boundary regions. This relates quantum information inequalities (e.g. Strong Subadditivity) to geometrical inequalities which can be given simple picture-proofs.

Since the dynamical version of AdS/CFT involves Lorentzian geometries, it is important to be able to prove the corresponding inequalities for asymptotically AdS geometries. In this case, we have to use extremal surfaces instead of minimal ones, making it more difficult to prove global inequalities. But by reformulating extremal surfaces in terms of an equivalent "maximin" variational principle, elegant proofs can be constructed. (Unlike the static case, these results require use of the null curvature condition.)

Based on arXiv:1211.3494.