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Gradient estimates, Bakry-Emery Ricci curvature and ellipticity for unbounded graph Laplacians

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arxiv 1807.10181 v2 pith:BYRGOBGF submitted 2018-07-26 math.DG

Gradient estimates, Bakry-Emery Ricci curvature and ellipticity for unbounded graph Laplacians

Matthias Keller , Florentin M\"unch This is my paper
classification math.DG
keywords bakry-emerycurvatureboundsellipticityestimatesgradientgraphlaplacians
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In this article, we prove gradient estimates under Bakry-Emery curvature bounds for unbounded graph Laplacians which satisfy an ellipticity assumption. As applications, we study completeness and finiteness of stochastically complete graphs under Bakry-Emery curvature bounds.

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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

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