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arXiv · 1605.05432

Global Poincar\'e inequality on Graphs via Conical Curvature-Dimension Conditions

Sajjad Lakzian·Zachary McGuirk
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Abstract

We introduce and study the conical curvature-dimension condition, $CCD(K,N)$, for graphs. We show that $CCD(K,N)$ provides necessary and sufficient conditions for the underlying graph to satisfy a sharp global Poincar\'e inequality which in turn translates to a sharp lower bound for the first eigenvalues of these graphs. Another application of the conical curvature-dimension analysis is finding a sharp estimate on the curvature of complete graphs.

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Sajjad Lakzian, Zachary McGuirk. 2016-05-18. Global Poincar\'e inequality on Graphs via Conical Curvature-Dimension Conditions. https://arxiv.org/abs/1605.05432

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