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 -rectifiable set, denoted by . Moreover we relate the size measure of T to the geometry of the tangent space .
@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}, pages = {79--100}, publisher = {Elsevier}, volume = {30}, number = {1}, year = {2013}, doi = {10.1016/j.anihpc.2012.06.002}, mrnumber = {3011292}, zbl = {1261.49013}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2012.06.002/} }
TY - JOUR AU - Ambrosio, Luigi AU - Ghiraldin, Francesco TI - Flat chains of finite size in metric spaces JO - Annales de l'I.H.P. Analyse non linéaire PY - 2013 SP - 79 EP - 100 VL - 30 IS - 1 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpc.2012.06.002/ DO - 10.1016/j.anihpc.2012.06.002 LA - en ID - AIHPC_2013__30_1_79_0 ER -
%0 Journal Article %A Ambrosio, Luigi %A Ghiraldin, Francesco %T Flat chains of finite size in metric spaces %J Annales de l'I.H.P. Analyse non linéaire %D 2013 %P 79-100 %V 30 %N 1 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpc.2012.06.002/ %R 10.1016/j.anihpc.2012.06.002 %G en %F 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, Volume 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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