How many cages midscribe an egg

• 成果类型: Article
• 署名作者: Liu, Jinsong; Zhou, Ze
• 署名单位: Chinese Academy of Sciences; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-015-0602-z
• 发表日期: 2016
• 页码: 655-673
• 关键词: circle patterns; packings; uniformization

摘要

The midscribability theorem, which was first proved by O. Schramm, states that: given a smooth strictly convex body and a convex polyhedron , there exists a convex polyhedron combinatorially equivalent to which midscribes . Here the word midscribe means that all its edges are tangent to the boundary surface of . By using the intersection number technique, together with the Teichmuller theory of packings, this paper provides an alternative approach to this theorem. Furthermore, by combining Schramm's method with the above ones, we obtain a rigidity result as well. That is, such a polyhedron is unique under the normalization condition.