Circle packings from tilings of the plane

被引：0

作者：

Rehwinkel, Philip ^{[1
]}

Whitehead, Ian ^{[1
]}

Yang, David ^{[1
]}

Yang, Mengyuan ^{[1
]}

机构：

[1] Swarthmore Coll, Dept Math & Stat, Swarthmore, PA 19081 USA

来源：

JOURNAL OF GEOMETRY | 2024年 / 115卷 / 01期

关键词：

Circle packing; Apollonian packing; Polyhedral packing; Koebe-Andreev-Thurston theorem;

D O I：

10.1007/s00022-024-00715-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce a new class of fractal circle packings in the plane, generalizing the polyhedral packings defined by Kontorovich and Nakamura. The existence and uniqueness of these packings are guaranteed by infinite versions of the Koebe-Andreev-Thurston theorem. We prove structure theorems giving a complete description of the symmetry groups for these packings. And we give several examples to illustrate their number-theoretic and group-theoretic significance.

引用

页数：28

共 43 条

[41] The Number of Configurations of Radii that Can Occur in Compact Packings of the Plane with Discs of n Sizes is Finite
Miek Messerschmidt
Discrete & Computational Geometry, 2024, 71 : 667 - 682
[42] ODED SCHRAMM: FROM CIRCLE PACKING TO SLE
Rohde, Steffen
ANNALS OF PROBABILITY, 2011, 39 (05) : 1621 - 1667
[43] From circle packing to covering on a sphere with antipodal constraints
Fowler, PW
Tarnai, T
Gáspár, Z
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2002, 458 (2025): : 2275 - 2287

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