多面体曲面和偏序集的组合里奇曲率
Combinatorial Ricci Curvature for Polyhedral Surfaces and Posets
摘要：
Forman的组合里奇曲率定义在CW复形的边缘处，并且仅利用复形中单元的面关系，不满足Gauss-Bonnet定理的模拟，并且不表现为与关于负曲率的光滑表面类似。我们将这种曲率推广到顶点和面上，使得组合里奇曲率的问题基本上得到了解决。讨论是在排名偏序集。
英文摘要：
The combinatorial Ricci curvature of Forman, which is defined at the edges of a CW complex, and which makes use of only the face relations of the cells in the complex, does not satisfy an analog of the Gauss-Bonnet Theorem, and does not behave analogously to smooth surfaces with respect to negative curvature. We extend this curvature to vertices and faces in such a way that the problems with combinatorial Ricci curvature are mostly resolved. The discussion is stated in terms of ranked posets.
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