Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the subinvariance of uniform domains in metric spaces   Suppose that $X$ and $Y$ are quasiconvex and complete metric spaces, that
$G\subset X$ and $G'\subset Y$ are domains, and that $f: G\to G'$ is a
homeomorphism. Our main result is the following subinvariance property of the
class of uniform domains: Suppose both $f$ and $f^{-1}$ are weakly
quasisymmetric mappings and $G'$ is a quasiconvex domain. Then the image $f(D)$
of every uniform subdomain $D$ in $G$ under $f$ is uniform. The subinvariance
of uniform domains with respect to freely quasiconformal mappings or
quasihyperbolic mappings is also studied with the additional condition that
both $G$ and $G'$ are locally John domains.

27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph