Harnack Inequality for Magnetic Graphs

2019/10/09 by Sawyer Jack Robertson, Robertson, Sawyer Jack
Mathematics · #05C22 #39A12 #Combinatorics (math.CO) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Graph theory and applications #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1910.04019

openalex publication_date 2019/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For magnetic graphs satisfying connection curvature dimension inequality CD^σ(n,κ), we prove a Harnack-type inequality for eigenfunctions of the graph magnetic Laplace operator in the manner of work done by Chung, Lin, Yau in 2014. Then we look at two applications; first a lower bound for the least eigenvalue in terms of curvature and extremal path/degree quantities, then to the magnetic Cheeger number of the graph.

Citations

• Structural balance: a generalization of Heider's theory.

Related

• Isoperimetric and Sobolev inequalities for magnetic graphs
• Harnack inequalities for graphs with non-negative Ricci curvature
• Eigenvalue Sums of Combinatorial Magnetic Laplacians on Finite Graphs
• Ricci curvature and eigenvalue estimates for the magnetic Laplacian on manifolds
• Harnack's inequality and Green functions on locally finite graphs