Harnack inequalities for graphs with non-negative Ricci curvature
Fan Chung, Yong Lin, Shing-Tung Yau
TL;DR
This paper proves a Harnack inequality for finite graphs with non-negative Ricci curvature and derives eigenvalue bounds, extending known results for Ricci flat graphs.
Contribution
It introduces a Harnack inequality for graphs with non-negative Ricci curvature and extends eigenvalue bounds beyond Ricci flat cases.
Findings
Established Harnack inequality for such graphs
Derived eigenvalue lower bounds
Extended previous Ricci flat graph results
Abstract
We establish a Harnack inequality for finite connected graphs with non-negative Ricci curvature. As a consequence, we derive an eigenvalue lower bound, extending previous results for Ricci flat graphs.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Differential Geometry Research · Geometry and complex manifolds