Rodin (1987) proved the Schwarz's lemma analog for the circle packings based on the hexagonal combinatorics. In this paper, we prove the Schwarz's lemma for the circle packings with the general combinatorics and our proof is more simpler than Rodin's proof. At the same time, we obtain a rigidity property for those packings with the general combinatorics.
Keywordscircle packing, discrete extremal length, the maximum principle, hyperbolic geometry
MSC(2000): 52C15, 30C35, 30C62, 30G25Citation: Huang X J, Liu J S, Shen L. Schwarz's lemma for the circle packings with the general combinatorics.