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

2012/03/23 by Wenger, Stefan
#Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1203.5330

Abstract

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.

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