Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hierarchically hyperbolic groups and uniform exponential growth   We give several sufficient conditions for uniform exponential growth in the
setting of virtually torsion-free hierarchically hyperbolic groups. For
example, any hierarchically hyperbolic group that is also acylindrically
hyperbolic has uniform exponential growth. In addition, we provide a
quasi-isometric characterization of hierarchically hyperbolic groups without
uniform exponential growth. To achieve this, we gain new insights on the
structure of certain classes of hierarchically hyperbolic groups. Our methods
give a new unified proof of uniform exponential growth for several examples of
groups with notions of non-positive curvature. In particular, we obtain the
first proof of uniform exponential growth for certain groups that act
geometrically on CAT(0) cubical spaces of dimension 3 or more. Under additional
hypotheses, we show that a quantitative Tits alternative holds for
hierarchically hyperbolic groups.

26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom