L_delta groups are almost convex and have a sub-cubic Dehn function

Torsion Subgroups of Groups with Cubic Dehn Function

We construct the first examples of finitely presented groups with cubic Dehn function containing a finitely generated infinite torsion subgroup. Moreover, we show that any infinite free Burnside group with sufficiently large odd exponent can be embedded as a subgroup of a finitely presented group with cubic Dehn function.

A Subgroup of a Direct Product of Free Groups whose Dehn Function has a Cubic Lower Bound

We establish a cubic lower bound on the Dehn function of a certain finitely presented subgroup of a direct product of 3 free groups.

The Geometry of the Handlebody Groups II: Dehn functions

We show that the Dehn function of the handlebody group is exponential in any genus $g\geq 3$. On the other hand, we show that the handlebody group of genus $2$ is cubical, biautomatic, and therefore has a quadratic Dehn function.

Identifying Dehn Functions of Bestvina--Brady Groups From Their Defining Graphs

Let $Γ$ be a finite simplicial graph such that the flag complex on $Γ$ is a $2$-dimensional triangulated disk. We show that with some assumptions, the Dehn function of the associated Bestvina--Brady group is either quadratic, cubic, or quartic. Furthermore, we can identify the Dehn function from the defining graph $Γ$.

On the Dehn functions of Kähler groups

We address the problem of which functions can arise as Dehn functions of Kähler groups. We explain why there are examples of Kähler groups with linear, quadratic, and exponential Dehn function. We then proceed to show that there is an example of a Kähler group which has Dehn function bounded below by a cubic function and above by $n^6$. As a consequence we obtain that for a compact Kähler manifold having non-positive holomorphic bisectional curvature does not imply having quadratic Dehn function.

Bestvina-Brady群的Dehn函数的完全分类

Complete classification of the Dehn functions of Bestvina-Brady groups

本文证明了每个有限表示的Bestvina-Brady群的Dehn函数增长为线性、二次、三次或四次多项式，并给出了确定多项式次数的显式判据，进而识别了阻碍某些Bestvina-Brady群具有CAT(0)结构的障碍。