Buser's inequality on infinite graphs

Shuang Liu

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arXiv · 1810.12003

Buser's inequality on infinite graphs

Shuang Liu

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Abstract

In this paper, we establish Buser type inequalities, i.e., upper bounds for eigenvalues in terms of Cheeger constants. We prove the Buser's inequality for an infinite but locally finite connected graph with Ricci curvature lower bounds. Furthermore, we derive that the graph with positive curvature is finite, especially for unbounded Laplacians. By proving Poincar\'e inequality, we obtain a lower bound on Cheeger constant in terms of positive curvature.

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Shuang Liu. 2018-10-29. Buser's inequality on infinite graphs. https://arxiv.org/abs/1810.12003

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