Abstract We introduce and study the conical curvature-dimension condition, CCD(K, N), for finite graphs.We show that CCD(K, N) provides necessary and sufficient conditions for the underlying graph to satisfy a sharp global Poincaré inequality which in turn translates to a sharp lower bound for the first eigenvalues of these graphs. Another application of the conical curvature-dimension analysis is finding a sharp estimate on the curvature of complete graphs

中文翻译：

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基于圆锥曲率维条件的图上的全局庞加莱不等式

摘要 我们介绍并研究了有限图的锥形曲率维条件 CCD(K, N)。我们证明 CCD(K, N) 为底层图满足尖锐的全局 Poincaré 不等式提供了充分必要条件turn 转换为这些图的第一个特征值的急剧下界。圆锥曲率维数分析的另一个应用是找到完整图曲率的精确估计