Journal
ADVANCES IN CALCULUS OF VARIATIONS
Volume 7, Issue 2, Pages 227-240Publisher
WALTER DE GRUYTER GMBH
DOI: 10.1515/acv-2012-0018
Keywords
Plateau's problem; area minimizers; Banach spaces; compactness
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Funding
- NSF grants [DMS 0956374, DMS 1056263]
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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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