  The purpose of this article is to prove existence of mass minimizing integral
currents with prescribed possibly non-compact boundary in all dual Banach
spaces and furthermore in certain spaces without linear structure, such as
injective metric spaces and Hadamard spaces. We furthermore prove a
weak$^*$-compactness theorem for integral currents in dual spaces of separable
Banach spaces. Our theorems generalize results of Ambrosio-Kirchheim, Lang, the
author, and recent results of Ambrosio-Schmidt.
