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The purpose of this article is to prove existence of mass minimizing integralcurrents with prescribed possibly non-compact boundary in all dual Banachspaces and furthermore in certain spaces without linear structure, such asinjective metric spaces and Hadamard spaces. We furthermore prove aweak$^*$-compactness theorem for integral currents in dual spaces of separableBanach spaces. Our theorems generalize results of Ambrosio-Kirchheim, Lang, theauthor, and recent results of Ambrosio-Schmidt.

Plateau's problem for integral currents in locally non-compact metric spaces