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arXiv · 1501.05839

Remarks on curvature dimension conditions on graphs

Florentin Münch
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Abstract

We show a connection between the $CDE'$ inequality and the $CDψ$ inequality. In particular, we introduce a $CD_ψ^φ$ inequality as a slight generalization of $CDψ$ which turns out to be equivalent to $CDE'$ with appropriate choices of $φ$ and $ψ$. 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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Florentin Münch. 2015-01-23. Remarks on curvature dimension conditions on graphs. https://arxiv.org/abs/1501.05839

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