基于圆锥曲率维数条件的图上的全局Poincaré不等式

Pub Date : 2018-02-16 DOI:10.1515/agms-2018-0002

Sajjad Lakzian, Zachary Mcguirk

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引用次数: 6

摘要

摘要引入并研究了有限图的圆锥曲率维条件CCD(K, N)。我们证明了CCD(K, N)为底层图满足尖锐全局poincarcarve不等式提供了充分必要条件，该不等式转化为这些图的第一特征值的尖锐下界。圆锥曲率维数分析的另一个应用是找到完全图曲率的一个尖锐估计

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A Global Poincaré inequality on Graphs via a Conical Curvature-Dimension Condition

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

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