The Bernstein problem, namely the problem of classifying all entire minimal hypergraphs in Euclidean spaces has played a crucial role in the development of Analysis throughout the whole course of the twentieth century. In this talk, I will discuss its natural extension to asymptotically flat manifolds, where it is motivated by the study of the large-scale structure of initial data sets for the Einstein field equation. I will first present the basic non-existence result and its relation to the asymptotic Plateau problem and then mention the application of similar techniques to the study of
1) large CMC spheres and isoperimetric domains (C.-Chodosh-Eichmair),
2) marginally outer-trapped surfaces (C.) and 3) the zero set of static potentials (Galloway-Miao). http://cvgmt.sns.it/seminar/451/
