TY - JOUR
T1 - Buser's inequality on infinite graphs
AU - Liu, Shuang
N1 - Publisher Copyright:
© 2019 Elsevier Inc.
PY - 2019/7/15
Y1 - 2019/7/15
N2 - 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 Poincaré inequality, we obtain a lower bound for Cheeger constant in terms of positive curvature.
AB - 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 Poincaré inequality, we obtain a lower bound for Cheeger constant in terms of positive curvature.
KW - Buser's inequality
KW - Cheeger constants
KW - Curvature-dimension inequality
KW - Infinite graph
UR - http://www.scopus.com/inward/record.url?scp=85063261197&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2019.03.023
DO - 10.1016/j.jmaa.2019.03.023
M3 - Article
AN - SCOPUS:85063261197
SN - 0022-247X
VL - 475
SP - 1416
EP - 1426
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
ER -