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arXiv · 1403.7768

Metric Currents and Alberti representations

Andrea Schioppa
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Abstract

We relate Ambrosio-Kirchheim metric currents to Alberti representations and Weaver derivations. In particular, given a metric current $T$, we show that if the module $\mathscr{X}(\|T\|)$ of Weaver derivations is finitely generated, then $T$ can be represented in terms of derivations; this extends previous results of Williams. Applications of this theory include an approximation of $1$-dimensional metric currents in terms of normal currents and the construction of Alberti representations in the directions of vector fields.

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Andrea Schioppa. 2014-03-30. Metric Currents and Alberti representations. https://arxiv.org/abs/1403.7768

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