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Curvature calculations for antitrees

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arxiv 1801.09400 v1 pith:PAZ3DRPS submitted 2018-01-29 math.CO

David Cushing , Shiping Liu , Florentin Münch , Norbert Peyerimhoff This is my paper · ORCID
classification math.CO
keywords curvatureantitreesdifferentgraphspositiveanaloguesarticlebakry-
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In this article we prove that antitrees with suitable growth properties are examples of infinite graphs exhibiting strictly positive curvature in various contexts: in the normalized and non-normalized Bakry-\'Emery setting as well in the Ollivier-Ricci curvature case. We also show that these graphs do not have global positive lower curvature bounds, which one would expect in view of discrete analogues of the Bonnet-Myers theorem. The proofs in the different settings require different techniques.

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  1. Nonnegative Bakry--\'Emery Curvature on Bounded-Degree Graphs Implies Volume Doubling and Poincar\'e Inequalities

    math.DG 2026-07 conditional novelty 8.0 of 10

    Connected bounded-degree graphs satisfying CD(0,∞) for the unnormalised Laplacian are volume doubling and satisfy scale-invariant L² Poincaré inequalities with dilation two.

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