Calculus of Variations and Geometric Measure Theory

L. Ambrosio - M. Katz

Flat currents modulo $p$ in metric spaces and filling radius inequalities

created by ambrosio on 19 May 2009
modified on 22 Jun 2009


Submitted Paper

Inserted: 19 may 2009
Last Updated: 22 jun 2009

Year: 2009


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 $*Z*_p$. We obtain isoperimetric inequalities modulo 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 modulo p in the homology class, and use the isoperimetric inequality to give lower bounds on the growth of their mass in balls.

Keywords: currents, isoperimetric inequality, Flat chains