The CDp Curvature Condition on a Graph

Xi XU; Wang SHEN; Linfeng WANG

doi:10.1007/s11464-021-0488-6

Frontiers of Mathematics ›› 2024, Vol. 19 ›› Issue (1) : 181 -192. DOI: 10.1007/s11464-021-0488-6

RESEARCH ARTICLE

The CD_p Curvature Condition on a Graph

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Abstract

In this paper we firstly prove that the CD_p curvature condition always satisfies for $p ≥ 2$ on any connected locally finite graph. We show this property does not hold for $1 < p < 2$ . We also derive a lower bound for the first nonzero eigenvalue of the p-Laplace operator on a connected finite graph with the CD_p(m, K) condition for the case that $1 < p ≤ 2, m > 2 (p − 1) 2 p$ and K > 0.

Keywords

p-Laplace operator / CD _p condition / graph / eigenvalue

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Xi XU, Wang SHEN, Linfeng WANG. The CD_p Curvature Condition on a Graph. Frontiers of Mathematics, 2024, 19(1): 181-192 DOI:10.1007/s11464-021-0488-6