We adapt the theory of currents in metric spaces, as developed by the first-mentioned author in collaboration with B. Kirchheim, to currents with coefficients in ℤp . We obtain isoperimetric inequalities mod (p) in Banach spaces and we apply these inequalities to provide a proof of Gromov’s filling radius inequality which applies also to nonorientable manifolds. With this goal in mind, we use the Ekeland principle to provide quasi-minimizers of the mass mod (p) in the homology class, and use the isoperimetric inequality to give lower bounds on the growth of their mass in balls.
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Luigi Ambrosio, Mikhail G. Katz, Flat currents modulo <var>p</var> in metric spaces and filling radius inequalities. Comment. Math. Helv. 86 (2011), no. 3, pp. 557–591DOI 10.4171/CMH/234