Remarks on curvature dimension conditions on graphs

被引：26

作者：

Muench, Florentin ^{[1
]}

机构：

[1] Univ Potsdam, Karl Liebknecht Str 24, D-14476 Potsdam, Germany

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2017年 / 56卷 / 01期

关键词：

05C81; 35K05; 53C21;

D O I：

10.1007/s00526-016-1104-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show a connection between the CDE' inequality introduced in Horn et al. (Volume doubling, Poincare inequality and Gaussian heat kernel estimate for nonnegative curvature graphs. arXiv: 1411.5087v2, 2014) and the CD psi inequality established in Munch (Li-Yau inequality on finite graphs via non-linear curvature dimension conditions. arXiv: 1412.3340v1, 2014). In particular, we introduce a CD psi phi inequality as a slight generalization of CD psi which turns out to be equivalent to CDE' with appropriate choices of. and psi. 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.

引用

页数：8