Fractional isoperimetric inequalities and subgroup distortion

1999/06/09 by Martin R. Bridson · 1 citation
Mathematics · Medicine · Materials Science · #Geometric and Algebraic Topology #Bone health and treatments #Quasicrystal Structures and Properties #Mathematics #Isoperimetric inequality #Distortion (music) #Combinatorics #Finitely-generated abelian group #Group (periodic table) #Finitely generated group #Pure mathematics #Function (biology)

paper · pdf · doi:10.1090/s0894-0347-99-00308-2

openalex publication_date 1999/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/15

Abstract

It is shown that there exist infinitely many non-integers r>2 such that the Dehn function of some finitely presented group is ≃ n^r. Explicit examples of such groups are constructed. For each rational number s≥ 1 pairs of finitely presented groups H⊂ G are constructed so that the distortion of H in G is ≃ n^s.

Citations

• There is only one gap in the isoperimetric spectrum
• A short proof that a subquadratic isoperimetric inequality implies a linear one.
• HYPERBOLICITY OF GROUPS WITH SUBQUADRATIC ISOPERIMETRIC INEQUALITY
• Isoperimetric and isodiametric functions of groups

Cited by

• Geometric group theory [wikipedia]