Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Isoperimetric inequalities, shapes of F{\o}lner sets and groups with
  Shalom's property ${H_{\mathrm{FD}}}$   We prove an isoperimetric inequality for groups. As an application, we obtain
lower bound on F{\o}lner functions in various nilpotent-by-cyclic groups. Under
a regularity assumption, we obtain a characterization of F{\o}lner functions of
these groups. As another application, we evaluate the asymptotics of the
F{\o}lner function of $Sym(\mathbb{Z})\rtimes {\mathbb{Z}}$. We construct new
examples of groups with Shalom's property $H_{\mathrm{FD}}$, in particular
among nilpotent-by-cyclic and lacunary hyperbolic groups. Among these examples
we find groups with property $H_{\mathrm{FD}}$, which are direct products of
lacunary hyperbolic groups and have arbitrarily large F{\o}lner functions.

14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph