数学
欧几里德几何
交叉口(航空)
拉普拉斯算子
边界(拓扑)
维数(图论)
德劳内三角测量
组合数学
分段
操作员(生物学)
纯数学
几何学
数学分析
生物化学
化学
抑制因子
转录因子
工程类
基因
航空航天工程
标识
DOI:10.1016/j.comgeo.2023.102063
摘要
This paper uses the technology of weighted triangulations to study discrete versions of the Laplacian on piecewise Euclidean manifolds. Given a collection of Euclidean simplices glued together along their boundary, a geometric structure on the Poincaré dual may be constructed by considering weights at the vertices. We show that this is equivalent to specifying sphere radii at vertices and generalized intersection angles at edges, or by specifying a certain way of dividing the edges. This geometric structure gives rise to a discrete Laplacian operator acting on functions on the vertices. We study these geometric structure in some detail, considering when dual volumes are nondegenerate, which corresponds to weighted Delaunay triangulations in dimension 2, and how one might find such nondegenerate weighted triangulations. Finally, we talk briefly about the possibilities of discrete Riemannian manifolds.
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