Resolving on 100 pc scales the UV-continuum in Lyman-$\alpha$ emitters
  between redshift 2 to 3 with gravitational lensing
  We present a study of seventeen LAEs at redshift 2$<z<$3 gravitationally
lensed by massive early-type galaxies (ETGs) at a mean redshift of
approximately 0.5. Using a fully Bayesian grid-based technique, we model the
gravitational lens mass distributions with elliptical power-law profiles and
reconstruct the UV-continuum surface brightness distributions of the background
sources using pixellated source models. We find that the deflectors are close
to, but not consistent with isothermal models in almost all cases, at the
$2\sigma$-level. We take advantage of the lensing magnification (typically
$\mu\simeq$ 20) to characterise the physical and morphological properties of
these LAE galaxies. From reconstructing the ultra-violet continuum emission, we
find that the star-formation rates range from 0.3 to 8.5 M$_{\odot}$ yr$^{-1}$
and that the galaxies are typically composed of several compact and diffuse
components, separated by 0.4 to 4 kpc. Moreover, they have peak star-formation
rate intensities that range from 2.1 to 54.1 M$_{\odot}$ yr$^{-1}$ kpc$^{-2}$.
These galaxies tend to be extended with major axis ranging from 0.2 to 1.8 kpc
(median 561 pc), and with a median ellipticity of 0.49. This morphology is
consistent with disk-like structures of star-formation for more than half of
the sample. However, for at least two sources, we also find off-axis components
that may be associated with mergers. Resolved kinematical information will be
needed to confirm the disk-like nature and possible merger scenario for the
LAEs in the sample.
