How many cages midscribe an egg

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• 作者：Jinsong Liu ; Ze Zhou
• 关键词：52B10 ; 52A15 ; 57Q99
• 刊名：Inventiones Mathematicae
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：203
• 期：2
• 页码：655-673
• 全文大小：508 KB
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• 作者单位：Jinsong Liu (1) (2)
  Ze Zhou (1) (2)
  
  1. HUA Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing, 100190, China
  2. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-1297

文摘

The midscribability theorem, which was first proved by O. Schramm, states that: given a smooth strictly convex body \(K\subset {\mathbb {R}}^{3}\) and a convex polyhedron \(P\), there exists a convex polyhedron \(Q\subset {\mathbb {R}}^3\) combinatorially equivalent to \(P\) which midscribes \(K\). Here the word “midscribe” means that all its edges are tangent to the boundary surface of \(K\). By using the intersection number technique, together with the Teichmüller 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. Mathematics Subject Classification 52B10 52A15 57Q99