Linear isoperimetric functions for surfaces in hyperbolic groups

TL;DR

This paper proves that hyperbolic groups have linear isoperimetric functions for all surface diagrams, extending previous results limited to discs and annuli, which has implications for understanding their geometric properties.

Contribution

It generalizes linear isoperimetric inequalities to all surface types in hyperbolic groups, broadening the scope of geometric group theory results.

Findings

Hyperbolic groups satisfy linear isoperimetric functions for all surface diagrams.

Extension of linear isoperimetric inequalities from discs and annuli to all surfaces.

Implications for the geometric understanding of hyperbolic groups.

Abstract

We show that word-hyperbolic groups satisfy linear isoperimetric functions for all homotopy types of surface diagrams. This generalises the linear isoperimetric functions for disc and annular diagrams.