Rigidity properties of the hypercube via Bakry-Émery curvature

DOI10.1007/s00208-022-02537-yarXiv1705.06789WikidataQ116244453 ScholiaQ116244453MaRDI QIDQ6191268

Norbert Peyerimhoff, Florentin Münch, Shiping Liu

Publication date: 9 February 2024

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.06789

zbMATH Keywords

Ricci curvatureRiemannian manifoldsLichnerowicz eigenvalue bound

Mathematics Subject Classification ID

Hypergraphs (05C65) Planar graphs; geometric and topological aspects of graph theory (05C10) Rigidity and flexibility of structures (aspects of discrete geometry) (52C25)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Synthetic theory of Ricci curvature bounds
• Volume growth, spectrum and stochastic completeness of infinite graphs
• Displacement convexity of entropy and related inequalities on graphs
• Equivalent semigroup properties for the curvature-dimension condition
• Ricci curvature of Markov chains on metric spaces
• A survey of the theory of hypercube graphs
• Another characterization of hypercubes
• Eigenvalue comparison theorems and its geometric applications
• A characterization of hypercubes
• Bakry-Émery curvature and diameter bounds on graphs
• Ricci curvature of finite Markov chains via convexity of the entropy
• Volume doubling, Poincaré inequality and Gaussian heat kernel estimate for non-negatively curved graphs
• Ricci curvature for metric-measure spaces via optimal transport
• Curvature and transport inequalities for Markov chains in discrete spaces
• On the geometry of metric measure spaces. I
• On the geometry of metric measure spaces. II
• Certain conditions for a Riemannian manifold to be isometric with a sphere
• Discrete Curvature and Abelian Groups
• Curvature aspects of graphs
• Curvature and Higher Order Buser Inequalities for the Graph Connection Laplacian
• Equivalent Properties of CD Inequality on Graph
• A Curved Brunn--Minkowski Inequality on the Discrete Hypercube, Or: What Is the Ricci Curvature of the Discrete Hypercube?
• Eigenvalue Ratios of Non-Negatively Curved Graphs
• The Graph Curvature Calculator and the Curvatures of Cubic Graphs
• Bakry–Émery Curvature Functions on Graphs
• Metric structures for Riemannian and non-Riemannian spaces. Transl. from the French by Sean Michael Bates. With appendices by M. Katz, P. Pansu, and S. Semmes. Edited by J. LaFontaine and P. Pansu

This page was built for publication: Rigidity properties of the hypercube via Bakry-Émery curvature