Marchese, Andrea Stuvard, Salvatore <jats:title>Abstract</jats:title><jats:p>In this paper, we prove that every equivalence class in the quotient group of integral 1-currents modulo <jats:italic>p</jats:italic> in Euclidean space contains an integral current, with quantitative estimates on its mass and the mass of its boundary. Moreover, we show that the validity of this statement for <jats:italic>m</jats:italic>-dimensional integral currents modulo <jats:italic>p</jats:italic> implies that the family of <jats:inline-formula id="j_acv-2016-0040_ineq_9999_w2aab3b7d666b1b6b1aab1c15b1b7Aa"><jats:alternatives><jats:tex-math>{(m-1)}</jats:tex-math></jats:alternatives></jats:inline-formula>-dimensional flat chains of the form <jats:italic>pT</jats:italic>, with <jats:italic>T</jats:italic> a flat chain, is closed with respect to the flat norm. In particular, we deduce that such closedness property holds for 0-dimensional flat chains, and, using a proposition from <jats:italic>The structure of minimizing hypersurfaces mod 4</jats:italic> by Brian White, also for flat chains of codimension 1.</jats:p> application/pdf https://sonar.ch/global/documents/284350 eng info:eu-repo/semantics/altIdentifier/doi/10.1515/acv-2016-0040 info:eu-repo/semantics/altIdentifier/issn/1864-8266 info:eu-repo/semantics/openAccess Advances in Calculus of Variations. - Walter de Gruyter GmbH. - 2018, vol. 11, no. 3, p. 309-323 Applied Mathematics Analysis On the structure of flat chains modulo p http://purl.org/coar/resource_type/c_6501