Flat chains of finite size in metric spaces
Luigi Ambrosio
Scuola Normale Superiore, Piazza Cavalieri 7, 56126 Pisa, ItalyFrancesco Ghiraldin
Scuola Normale Superiore, Piazza Cavalieri 7, 56126 Pisa, Italy
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Abstract
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 .
Cite this article
Luigi Ambrosio, Francesco Ghiraldin, Flat chains of finite size in metric spaces. Ann. Inst. H. Poincaré Anal. Non Linéaire 30 (2013), no. 1, pp. 79–100
DOI 10.1016/J.ANIHPC.2012.06.002