Schwarz’s lemma for the circle packings with the general combinatorics  

作　　者：XiaoJun Huang JinSong Liu Liang Shen 

出　　处：《Science China Mathematics》2010年第2期277-290,共14页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos.10701084, 10501046);the Natural Science Foundation of Chongqing, China (Grant No. CSTC2008BB0151)

摘　　要：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.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.

关 键 词：circle PACKING discrete EXTREMAL length the maximum PRINCIPLE HYPERBOLIC geometry 

分 类 号：N[自然科学总论]