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 p by Brian White, also for flat chains of codimension 1.

On the structure of flat chains modulo p / A. Marchese, S. Stuvard. - In: ADVANCES IN CALCULUS OF VARIATIONS. - ISSN 1864-8258. - 11:3(2018 Jul), pp. 309-323.

On the structure of flat chains modulo p

S. Stuvard
2018

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 p by Brian White, also for flat chains of codimension 1.
Integral currents mod p; flat chains mod p
Settore MAT/05 - Analisi Matematica
19-apr-2017
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/850381
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