The aim of the talk will be to review in a pedagogical way how the ‘AdS-CFT correspondence’, which derived originally in string theory, turns certain questions in quantum field theory into geometric problems. Of most probably interest to the audience are a subclass of these problems which are related to the geometry of asymptotically hyperbolic Einstein spaces. I will then discuss a specific example which nicely illustrates how simple geometric analysis provides a very interesting result for certain quantum field theories. On the physics side this results relates to the behaviour of the `Casimir energy’ of the field theory. From the geometric perspective the result is related to a necessary condition for existence of asymptotically hyperbolic Einstein spaces with a specific isometry.