Spectrally positive Bakry-Émery Ricci curvature on graphs

DOI10.1016/J.MATPUR.2020.03.008zbMath1450.05090arXiv1912.06438OpenAlexW3012109199MaRDI QIDQ2204943

Florentin Münch, Christian Rose

Publication date: 16 October 2020

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.06438

zbMATH Keywords

heat equationgraph LaplacianRicci curvature on graphsvariable Ricci curvature

Mathematics Subject Classification ID

Heat equation (35K05) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Graph theory (05C99) Discrete differential geometry (53A70)

Related Items (4)

Stability of metric measure spaces with integral Ricci curvature bounds ⋮ On the Lichnerowicz estimate for Laplacians on graphs under spectral curvature assumptions ⋮ Eigenvalue estimates for Kato-type Ricci curvature conditions ⋮ Bakry-Émery curvature on graphs as an eigenvalue problem

Cites Work

• Unnamed Item
• Geodesic convexity of the relative entropy in reversible Markov chains
• Harmonic functions on manifolds whose large spheres are small
• Absorption semigroups, their generators, and Schrödinger semigroups
• Li-Yau inequality on finite graphs via non-linear curvature dimension conditions
• Poincaré, modified logarithmic Sobolev and isoperimetric inequalities for Markov chains with non-negative Ricci curvature
• Li-Yau gradient estimate for compact manifolds with negative part of Ricci curvature in the Kato class
• Bakry-Émery curvature and diameter bounds on graphs
• Ricci curvature of finite Markov chains via convexity of the entropy
• Perturbation of Dirichlet forms by measures
• Heat kernel upper bound on Riemannian manifolds with locally uniform Ricci curvature integral bounds
• Distance bounds for graphs with some negative Bakry-Émery curvature
• Harnack inequalities for graphs with non-negative Ricci curvature
• Ricci curvature of metric spaces
• Buser's inequality on infinite graphs
• Discrete Curvature and Abelian Groups
• The Kato class on compact manifolds with integral bounds on the negative part of Ricci curvature
• A note on the isoperimetric constant
• Curvature and Higher Order Buser Inequalities for the Graph Connection Laplacian
• Eigenvalue Ratios of Non-Negatively Curved Graphs

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