Some fine properties of currents and applications to distributional Jacobians

Camillo De Lellis

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Submission date: 06. Nov. 2000
Pages: 31
published in: Proceedings of the Royal Society of Edinburgh / A, 132 (2002) 4, p. 815-842 
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Abstract:
We study fine properties of currents in the framework of geometric measure theory on metric spaces developed by Ambrosio and Kirchheim in [1] and we prove a rectifiability criterion for flat currents of finite mass. We apply these tools to study the structure of the dis-tributional Jacobians of functions in the space BnV, defined by Jerrard and Soner in [2]. We define the subspace of special functions of bounded higher variation and we prove a closure theorem.

[1] Ambrosio L., Kirchheim B. Currents on metric spaces. Mat. Annalen. To appear.
[2] Jerrard L., Soner M. Functions of higher bounded variation. Forthcoming.