Flat chains of finite size in metric spaces

Ambrosio, Luigi; Ghiraldin, Francesco

doi:10.1016/j.anihpc.2012.06.002

Ambrosio, Luigi ; Ghiraldin, Francesco

Annales de l'I.H.P. Analyse non linéaire, Tome 30 (2013) no. 1, pp. 79-100.

Résumé

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 ${Tan}^{(k)} (𝑠𝑒𝑡 (T), x)$ .

MR Zbl | 1 citation dans Numdam

DOI : 10.1016/j.anihpc.2012.06.002

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     author = {Ambrosio, Luigi and Ghiraldin, Francesco},
     title = {Flat chains of finite size in metric spaces},
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     pages = {79--100},
     publisher = {Elsevier},
     volume = {30},
     number = {1},
     year = {2013},
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     zbl = {1261.49013},
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     url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2012.06.002/}
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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://archive.numdam.org/articles/10.1016/j.anihpc.2012.06.002/

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