论文标题
在Möbius变换和质量圆周的情况下，多层体积的变化
Change of polytope volumes under Möbius transformations and the circumcenter of mass
论文作者
论文摘要
简单多层$ p $的质量的周围定义如下：三角元素$ p $，分配给每个单纯子的圆周中心，重量等于单纯形的体积，然后找到所得的点质量系统的质量中心。 SO获得的点与三角剖分无关。 本注的目的是给出不依赖三角剖分的质量的定义。为此，我们研究了Möbius变换下的多体体积如何变化。
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.
