JournalscmhVol. 86, No. 3pp. 557–591

Flat currents modulo <var>p</var> in metric spaces and filling radius inequalities

  • Luigi Ambrosio

    Scuola Normale Superiore, Pisa, Italy
  • Mikhail G. Katz

    Bar-Ilan University, Ramat-Gan, Israel
Flat currents modulo <var>p</var> in metric spaces and filling radius  inequalities cover
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Abstract

We adapt the theory of currents in metric spaces, as developed by the first-mentioned author in collaboration with B. Kirchheim, to currents with coefficients in ℤp . We obtain isoperimetric inequalities mod (p) in Banach spaces and we apply these inequalities to provide a proof of Gromov’s filling radius inequality which applies also to nonorientable manifolds. With this goal in mind, we use the Ekeland principle to provide quasi-minimizers of the mass mod (p) in the homology class, and use the isoperimetric inequality to give lower bounds on the growth of their mass in balls.

Cite this article

Luigi Ambrosio, Mikhail G. Katz, Flat currents modulo <var>p</var> in metric spaces and filling radius inequalities. Comment. Math. Helv. 86 (2011), no. 3, pp. 557–591

DOI 10.4171/CMH/234