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Equivalent Properties of CD Inequality on Graph

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arxiv 1512.02677 v1 pith:7NV6EQYN submitted 2015-12-06 math.CO math.DG

Yong Lin , Shuang Liu This is my paper
classification math.COmath.DG
keywords equivalentconditionscurvature-dimensionestimategradientgraphinequalitiesinequality
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abstract

We study some equivalent properties of the curvature-dimension conditions $CD(n,K)$ inequality on infinite, but locally finite graph. These equivalences are gradient estimate, Poincar\'e type inequalities and reverse Poincar\'e inequalities. And we also obtain one equivalent property of gradient estimate for a new notion of curvature-dimension conditions $CDE'(\infty, K)$ at the same assumption of graphs.

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  1. Nonnegative Bakry--\'Emery Curvature on Bounded-Degree Graphs Implies Volume Doubling and Poincar\'e Inequalities

    math.DG 2026-07 conditional novelty 8.0 of 10

    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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