Harnack Inequality for Magnetic Graphs
Abstract
For magnetic graphs satisfying connection curvature dimension inequality CDσ(n,), 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.
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