Published Paper
Inserted: 18 jul 2016
Last Updated: 27 jun 2019
Journal: Adv. Calc. Var.
Volume: 11
Number: 3
Pages: 309-323
Year: 2018
Doi: 10.1515/acv-2016-0040
Abstract:
In this paper, we prove that every equivalence class in the quotient group of integral $1$-currents modulo $p$ 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 $m$-dimensional integral currents modulo $p$ implies that the family of $(m-1)$-dimensional flat chains of the form $pT$, with $T$ 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 "The structure of minimizing hypersurfaces mod $4$" by Brian White, also for flat chains of codimension $1$.
Keywords: Integral currents mod(p), Flat chains mod(p).
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