  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.
