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Buser's inequality on infinite graphs

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arxiv 1810.12003 v1 pith:6UHR7C4O submitted 2018-10-29 math.DG math.APmath.SP

Buser's inequality on infinite graphs

Shuang Liu This is my paper
classification math.DG math.APmath.SP
keywords busercurvatureinequalityboundscheegerfinitegraphinfinite
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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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