Flat chains of finite size in metric spaces
Annales de l'I.H.P. Analyse non linéaire, Tome 30 (2013) no. 1, pp. 79-100.

In this paper we investigate the notion of flat current in the metric spaces setting, and in particular we provide a definition of size of a flat current with possibly infinite mass. Exploiting the special nature of the 0-dimensional slices and the theory of metric-space valued BV functions we prove that a k-current with finite size T sits on a countably ℋ k -rectifiable set, denoted by 𝑠𝑒𝑡(T). Moreover we relate the size measure of T to the geometry of the tangent space Tan (k) (𝑠𝑒𝑡(T),x).

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     author = {Ambrosio, Luigi and Ghiraldin, Francesco},
     title = {Flat chains of finite size in metric spaces},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {79--100},
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Ambrosio, Luigi; Ghiraldin, Francesco. Flat chains of finite size in metric spaces. Annales de l'I.H.P. Analyse non linéaire, Tome 30 (2013) no. 1, pp. 79-100. doi : 10.1016/j.anihpc.2012.06.002. http://www.numdam.org/articles/10.1016/j.anihpc.2012.06.002/

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