Flat chains of finite size in metric spaces
Annales de l'I.H.P. Analyse non linéaire, Tome 30 (2013) no. 1, p. 79-100
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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 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).
@article{AIHPC_2013__30_1_79_0,
     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},
     publisher = {Elsevier},
     volume = {30},
     number = {1},
     year = {2013},
     pages = {79-100},
     doi = {10.1016/j.anihpc.2012.06.002},
     zbl = {1261.49013},
     mrnumber = {3011292},
     language = {en},
     url = {http://http://www.numdam.org/item/AIHPC_2013__30_1_79_0}
}
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/item/AIHPC_2013__30_1_79_0/

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