Back
Full-text
Journal article

On the structure of flat chains modulo p

  • Marchese, Andrea Universität Zürich, Winterthurerstrasse 190, CH-8057Zürich, Switzerland
  • Stuvard, Salvatore Universität Zürich, Winterthurerstrasse 190, CH-8057Zürich, Switzerland
Published in:
  • Advances in Calculus of Variations. - Walter de Gruyter GmbH. - 2018, vol. 11, no. 3, p. 309-323
Applied Mathematics
Analysis
English AbstractIn 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.
Language
  • English
Open access status
green
Identifiers
Persistent URL
https://sonar.ch/global/documents/284350
Statistics
Document views: 20 File downloads:
  • Full-text: 0