Abstract
In this paper we firstly prove that the CDp 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 CDp(m, K) condition for the case that \(1 < p \le 2,\,\,m > {{2{{(p - 1)}^2}} \over p}\) and K > 0.
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Acknowledgements
The corresponding author was partially supported by the Natural Science Foundation of Nantong City, Jiangsu Province (Heat kernel estimate, geometric functional and several related questions on the graph).
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Xu, X., Shen, W. & Wang, L. The CDp Curvature Condition on a Graph. Front. Math 19, 181–192 (2024). https://doi.org/10.1007/s11464-021-0488-6
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DOI: https://doi.org/10.1007/s11464-021-0488-6