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

Stefan Wenger

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arXiv · 1203.5330

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

Stefan Wenger

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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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BibTeX RIS

Stefan Wenger. 2012-03-23. Plateau's problem for integral currents in locally non-compact metric spaces. https://arxiv.org/abs/1203.5330

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