从多边形空间到多面体空间
From spaces of polygons to spaces of polyhedra following Bavard, Ghys and Thurston
摘要：
在W的工作之后。P. Thurston，C. Bavard和Bavard。吉斯从欧氏多边形的变形空间中构造了特殊的双曲多面体。我们提出这种结构作为一个简单的混合体积理论的结果。这些多面体的胶合可以等距嵌入到由Thurston从欧氏多面体的变形空间构造的复双曲锥流形中。这样就有可能推导出P. Deligne和G. D.莫斯托
英文摘要：
After work of W. P. Thurston, C. Bavard and É. Ghys constructed particular hyperbolic polyhedra from spaces of deformations of Euclidean polygons. We present this construction as a straightforward consequence of the theory of mixed-volumes. The gluing of these polyhedra can be isometrically embedded into complex hyperbolic cone-manifolds constructed by Thurston from spaces of deformations of Euclidean polyhedra. It is then possible to deduce the metric structure of the spaces of polygons embedded in complex hyperbolic orbifolds discovered by P. Deligne and G. D. Mostow.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
