Remarks on curvature dimension conditions on graphs
Remarks on curvature dimension conditions on graphs
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DOI：
10.1007/s00526-016-1104-6
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发表时间：
2017-01
影响因子：
2.1
通讯作者：
Florentin Münch
中科院分区：
文献类型：
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作者：
Florentin Münch
我们证明了Horn等人（Volume doubling，Poincaré inequality and Gaussian heat kernel estimate for nonnegative curvature graphs.） arXiv：1411.5087v2 ，2014）和Münch建立的不等式（Li-Yau不等式在有限图上通过非线性曲率维数条件. arXiv：1412.3340v1 ，2014）。特别是，我们引入了不等式作为的一个轻微的推广，结果证明它与和的适当选择等价。利用这一点，我们证明了这个不等式蕴涵了图上的经典CD不等式，并且证明了曲率有界为零的不等式在Ricci平坦图上成立。
We show a connection between theinequality introduced in Horn et al. (Volume doubling, Poincaré inequality and Gaussian heat kernel estimate for nonnegative curvature graphs. arXiv:1411.5087v2 , 2014) and theinequality established in Münch (Li–Yau inequality on finite graphs via non-linear curvature dimension conditions. arXiv:1412.3340v1 , 2014). In particular, we introduce ainequality as a slight generalization ofwhich turns out to be equivalent towith appropriate choices ofand. We use this to prove that theinequality implies the classicalCDinequality on graphs, and that theinequality with curvature bound zero holds on Ricci-flat graphs.