Flat currents modulo <var>p</var> in metric spaces and filling radius inequalities
Luigi AmbrosioScuola Normale Superiore, Pisa, Italy
Mikhail G. KatzBar-Ilan University, Ramat-Gan, Israel
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. 557–591DOI 10.4171/CMH/234