Harnack Inequality for Magnetic Graphs

Abstract

For magnetic graphs satisfying connection curvature dimension inequality $C{D}^{\sigma }(n,\kappa )$, 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.

10 pages