  The notion of circle packings has been explored intensively since Thurston
proposed it as an approximation to conformal maps. One of the fundamental
questions about circle packings is whether it converges to the Riemann mapping
if the radius of the circles tends to zero. In this paper, we prove the
convergence of circle packings to the maps induced by the uniformization
theorem in a different sense proposed by Gu-Luo-Wu for surfaces of genus one.
This is the first result of the convergence of circle packings on surfaces with
nontrivial topology.
