Buser's inequality on infinite graphs
Differential Geometry
2018-10-30 v1 Analysis of PDEs
Spectral Theory
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.
Keywords
Cite
@article{arxiv.1810.12003,
title = {Buser's inequality on infinite graphs},
author = {Shuang Liu},
journal= {arXiv preprint arXiv:1810.12003},
year = {2018}
}