Higher-dimensional linear isoperimetric inequalities in hyperbolic groups

It is shown that every word hyperbolic group satisfies linear homological isoperimetric inequalities for k-cycles for all k ≥ 1. According to a remark of S. Gersten, this has been open, except for the case of real or rational coefficients settled recently by I. Mineyev. The idea of the proof is simply to make use of the quasi-isometric embedding theorem for Gromov hyperbolic spaces of M. Bonk and O. Schramm and the well-known linear isoperimetric inequalities for real hyperbolic space.