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arXiv · 2601.16010

A brief note about p-curvature on graphs

Chunyang Hu
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Abstract

In this paper, we consider Wang's $CD_p(m,K)$ condition on graphs, which depends on the $p$-Laplacian $Δ_p$ for $p>1$ and is an extension of the classical Bakry-Émery $CD(m,K)$ curvature dimension condition. We calculate several examples including paths, cycles and star graphs, and we show that the $p$-curvature is non-negative at some vertices in the case $p\geq 2$, while it approaches to $-\infty$ in the case of $1 2$. As a consequence, an analogous proof that non-negative curvature is preserved under taking Cartesian products is not possible for $p > 2$.

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Chunyang Hu. 2026-01-22. A brief note about p-curvature on graphs. https://arxiv.org/abs/2601.16010

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