Equivalent Properties of CD Inequality on Graph
Combinatorics
2015-12-10 v1 Differential Geometry
Abstract
We study some equivalent properties of the curvature-dimension conditions 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 at the same assumption of graphs.
Keywords
Cite
@article{arxiv.1512.02677,
title = {Equivalent Properties of CD Inequality on Graph},
author = {Yong Lin and Shuang Liu},
journal= {arXiv preprint arXiv:1512.02677},
year = {2015}
}
Comments
13 pages