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Rectifiability of flat chains in Banach spaces with coefficients in Z p

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Abstract

In this paper we study the behaviour of a class of currents with coefficients in Z p in metric spaces, obtained by taking a suitable quotient of currents with coefficients in Z. We prove under fairly general assumption on the ambient space the rectifiability of the so-called slice mass, and under more restrictive assumptions the rectifiability of the mass measure.

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Authors and Affiliations

  1. Scuola Normale Superiore, Piazza Cavalieri 7, 56100, Pisa, Italy

    Luigi Ambrosio

  2. University of Illinois at Chicago, 851 S. Morgan Street, Chicago, IL, 60607-7045, USA

    Stefan Wenger

Authors
  1. Luigi Ambrosio
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  2. Stefan Wenger
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Corresponding author

Correspondence to Luigi Ambrosio.

Additional information

L. Ambrosio’s work was partially supported by a MIUR PRIN06 grant. S. Wenger’s work was partially supported by NSF grant DMS 0707009.

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Ambrosio, L., Wenger, S. Rectifiability of flat chains in Banach spaces with coefficients in Z p . Math. Z. 268, 477–506 (2011). https://doi.org/10.1007/s00209-010-0680-y

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  • DOI: https://doi.org/10.1007/s00209-010-0680-y

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