  We study the mass-size relation of quiescent galaxies across various
environments, with a particular focus on its environmental dependence at the
low-mass part of $\log(M_\mathrm{star}/M_{\odot})\lesssim10.0$. Our sample
consists of 13,667 quiescent galaxies with
$\log(M_\mathrm{star}/M_{\odot})\ge9.4$ and $0.01<z<0.04$ from the Sloan
Digital Sky Survey. We find that the mass-size relation of low-mass quiescent
galaxies (LQGs) with $\log(M_\mathrm{star}/M_{\odot})\lesssim10.0$ depends on
their environment, with LQGs in the highest-density environments exhibiting an
average size $\sim70\%$ larger than those in isolated environments. Moreover,
the slope of the mass-size relation for LQGs in high-density environments is
significantly shallower than that of their counterparts in isolated
environments. This is in contrast with high-mass quiescent galaxies with
$\log(M_\mathrm{star}/M_{\odot})\gtrsim10.5$ that show a nearly identical
mass-size relation across all environments. Combined with additional
discoveries that the mass-size relation slopes of LQGs and star-forming
galaxies are similar to each other in high-density environments, and that LQGs
in higher-density environments exhibit more disk-like structures, our results
support the idea that LQGs in high-density environments have evolved from
star-forming galaxies through environmental effects, which are capable of
causing their quenching and transformation into quiescent galaxies. With the
aid of an analysis of merger rates for simulated galaxies from a cosmological
galaxy formation simulation, we suggest that the steep slope and low
normalization of the mass-size relation of LQGs in the lowest-density
environments may originate from recent gas-rich mergers, which occur over 10-30
times more frequently in the progenitors of LQGs in the lowest-density
environments than in their counterparts in high-density environments at low
redshifts.
