Complete Classification of the Dehn Functions of Bestvina–Brady Groups

Journal article

We prove that the Dehn function of every finitely presented Bestvina–Brady group grows as a linear, quadratic, cubic, or quartic polynomial. In fact, we provide explicit criteria on the defining graph to determine the degree of this polynomial. As a consequence, we identify an obstruction that prevents certain Bestvina–Brady groups from admitting a CAT(0) structure.

Authors: Chang, Y; García-Mejía, J; Migliorini, M

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer
• Journal: Geometric And Functional Analysis
• Volume: 36
• Issue: 1
• Pages: 1-58
• Publication date: 2026-02-02
• Acceptance date: 2025-12-23
• DOI: 10.1007/s00039-026-00731-7
• EISSN: 1420-8970
• ISSN: 1016443X, 1016-443X
• Language: English
• Keywords: Filling invariants; 51F30; 20F05; Bestvina–Brady groups; 20F38; 20F65; Dehn functions; Asymptotic cones; Subgroups of right-angled Artin groups; 20F69