多胞体在Möbius变换下的体积变化与质心外接圆
Change of polytope volumes under Möbius transformations and the circumcenter of mass
摘要：
一个单纯多胞形$P$的外心质量定义如下：三角化$P$，分配给每个单形的外心，其权重等于单形的体积，然后找到所得到的点质量系统的质心。这样获得的点与三角测量无关。本说明的目的是给出一个不依赖于三角测量的外心的定义。要做到这一点，我们研究如何体积的多面体下莫比乌斯变换的变化。
英文摘要：
The circumcenter of mass of a simplicial polytope $P$ is defined as follows: triangulate $P$, assign to each simplex its circumcenter taken with weight equal to the volume of the simplex, and then find the center of mass of the resulting system of point masses. The so obtained point is independent of the triangulation. The aim of the present note is to give a definition of the circumcenter of mass that does not rely on a triangulation. To do so we investigate how volumes of polytopes change under Möbius transformations.
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。
