发表机构
TU Dresden（德累斯顿工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明单纯形最小立体角在任意维度均为形状度量，并给出其与丰满度的最优不等式，推广了最小角条件。
AI 中文摘要
本文证明了单纯形的最小立体角在任何维度下都是一个形状度量。虽然这在二维和三维中已知，但高维推广是新的。我们证明了非退化单纯形的最小立体角与其丰满度之间的不等式。在依赖于维度的常数范围内，丰满度由上界为最小立体角，下界为最小立体角的平方。这些指数在三维及更高维度是最优的。因此，这项工作推广了最小角条件。我们还回顾了几种单纯形形状度量及其相互关系。
英文摘要
The minimum solid angle of a simplex is shown to be a shape measure in any dimension. While this has been known in dimensions two and three, the higher-dimensional generalization is new. We prove inequalities between the minimum solid angle of a non-degenerate simplex and its fullness. Up to dimension-dependent constants, the fullness is bounded from above by the minimum solid angle and from below by the square of the minimum solid angle. The exponents are optimal for three and higher dimensions. This work therefore generalizes the minimum angle condition. We also review several simplex shape measures and their relationships.
Comments16 pages. Submitted. Comments welcome
