One of the main obstacles regarding Bakry–Emery curvature on graphs is that the results require a global uniform lower curvature bounds where no exception sets are allowed. We overcome this obstacle by introducing the perpetual cutoff method. As applications, we prove gradient estimates only requiring curvature bounds on parts of the graph. Moreover, we sharply upper bound the distance to the exception set for graphs having uniformly positive Bakry–Emery curvature everywhere but on the exception set.

中文翻译：

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永久截止法和离散 Ricci 曲率界（有例外）

图上 Bakry-Emery 曲率的主要障碍之一是结果需要全局统一的曲率下界，其中不允许任何例外集。我们通过引入永久切断方法克服了这个障碍。作为应用，我们证明梯度估计仅需要图的部分曲率边界。此外，对于除了例外集以外的所有地方都具有一致正 Bakry-Emery 曲率的图，我们对到例外集的距离进行了大幅上限。