English

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 CD(n,K)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)CDE'(\infty, K) 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

R2 v1 2026-06-22T12:04:45.625Z