  Bowers and Stephenson introduced the notion of inversive distance circle
packings as a natural generalization of Thurston's circle packings. They
conjectured that discrete conformal maps induced by inversive distance circle
packings converge to the Riemann mapping. Motivated by the recent work of
Luo-Sun-Wu, we prove Bowers-Stephenson's conjecture for Jordan domains by
establishing a maximal principle, an infinite rigidity theorem, and a
solvability theorem of certain prescribing combinatorial curvature problems for
inversive distance circle packings.
