图上曲率维数不等式的若干等价性质

Equivalent Properties of CD Inequalities on Graphs

本文研究局部有限图上的曲率维数不等式CD（n，K）的若干等价性质，包括梯度估计、Poincare不等式和逆Poincare不等式．还得到了局部有限图上的修正曲率维数不等式CDE’（∞，K）的其中一个等价性质，即梯度估计．

We study some equivalent properties of the curvature dimension inequality CD（n, K） on locally finite graphs. These equivalences are gradient estimate, Poincare type inequalities and reverse Poincare inequalities. We also obtain one equivalent property of gradient estimate for a new notion of curvature dimension inequality CDE＇（∞, K） at the same assumption on graphs.