Theorem: [KAT, Koebe-Andreev-Thurston] Given any triangulation K of a topological sphere, there exists a univalent circle packing PK of the Riemann sphere having the combinatorics of K. Moreover, PK is unique up to Mobius transformations and inversion.
Theorem: Given a triangulation K of any oriented topological surface S, there exists a conformal structure on S and a univalent circle packing PK in its intrinsic metric, so that PK “fills”S. Moreover, the conformal structure is unique and PK is unique up to its conformal automorphisms.
Theorem: [Schramm/He] Given any Jordan region A, there exists a univalent circle packing with heptagonal combinatorics which fills A. Moreover, the packing is unique subject to standard normalization.
[复制链接]
辽公网安备21021102000973号
发表于 2012-6-28 10:46:15
QQ好友和群
QQ空间
腾讯微博
腾讯朋友
收藏
分享
楼主