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Remarks on curvature dimension conditions on graphs
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Remarks on curvature dimension conditions on graphs
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We show a connection between the $CDE'$ inequality and the $CD\psi$ inequality. In particular, we introduce a $CD_\psi^\varphi$ inequality as a slight generalization of $CD\psi$ which turns out to be equivalent to $CDE'$ with appropriate choices of $\varphi$ and $\psi$. We use this to prove that the $CDE'$ inequality implies the classical $CD$ inequality on graphs, and that the $CDE'$ inequality with curvature bound zero holds on Ricci-flat graphs.
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Cited by 1 Pith paper
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Nonnegative Bakry--\'Emery Curvature on Bounded-Degree Graphs Implies Volume Doubling and Poincar\'e Inequalities
Connected bounded-degree graphs satisfying CD(0,∞) for the unnormalised Laplacian are volume doubling and satisfy scale-invariant L² Poincaré inequalities with dilation two.
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