Flat currents modulo p in metric spaces and filling radius inequalities

2011/06/01 by Luigi Ambrosio, Mikhail G. Katz · 1 citation
Mathematics · Computer Science · #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Topological and Geometric Data Analysis #Isoperimetric inequality #Mathematics #Modulo #Inequality #Isoperimetric dimension #RADIUS #Pure mathematics #Class (philosophy) #Metric space #Metric (unit) #Mathematical analysis #Discrete mathematics #Computer science

paper · pdf · doi:10.4171/cmh/234

openalex publication_date 2011/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 ℤ_p . 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.

Citations

• Hyperellipticity and Klein bottle companionship in systolic geometry
• E7, Wirtinger inequalities, Cayley 4-form, and homotopy
• Systolic inequalities and minimal hypersurfaces
• Loewner's torus inequality with isosystolic defect
• Rectifiability of flat chains in Banach spaces with coefficients in Z_p
• Relative systoles of relative-essential 2-complexes

Cited by

• Gromov's systolic inequality for essential manifolds [wikipedia]