Abstract
We study some equivalent properties of the curvature dimension inequality CD(n,K) on locally finite graphs. These equivalences are gradient estimate, Poincaré type inequalities and reverse Poincaré inequalities. We also obtain one equivalent property of gradient estimate for a new notion of curvature dimension inequality CDE (∞,K) at the same assumption on graphs.
| Translated title of the contribution | Equivalent Properties of CD Inequalities on Graphs |
|---|---|
| Original language | Chinese (Traditional) |
| Pages (from-to) | 431-440 |
| Number of pages | 10 |
| Journal | Acta Mathematica Sinica, Chinese Series |
| Volume | 61 |
| Issue number | 3 |
| Publication status | Published - 1 May 2018 |
| Externally published | Yes |