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 Poincaré inequality, we obtain a lower bound for Cheeger constant in terms of positive curvature.
Original language | English |
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Pages (from-to) | 1416-1426 |
Number of pages | 11 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 475 |
Issue number | 2 |
DOIs | |
Publication status | Published - 15 Jul 2019 |
Externally published | Yes |
Keywords
- Buser's inequality
- Cheeger constants
- Curvature-dimension inequality
- Infinite graph