Equivalent Properties of CD Inequality on Graph
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'(∞, K) at the same assumption of graphs.
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