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arXiv · 1910.04019

Harnack Inequality for Magnetic Graphs

Sawyer Jack Robertson
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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.

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Sawyer Jack Robertson. 2019-10-10. Harnack Inequality for Magnetic Graphs. https://arxiv.org/abs/1910.04019

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