General Cheeger inequalities for p-Laplacians on graphs
- We prove Cheeger inequalities for p-Laplacians on finite and infinite weighted graphs. Unlike in previous works, we do not impose boundedness of the vertex degree, nor do we restrict ourselves to the normalized Laplacian and, more generally, we do not impose any boundedness assumption on the geometry. This is achieved by a novel definition of the measure of the boundary which uses the idea of intrinsic metrics. For the non-normalized case, our bounds on the spectral gap of p-Laplacians are already significantly better for finite graphs and for infinite graphs they yield non-trivial bounds even in the case of unbounded vertex degree. We, furthermore, give upper bounds by the Cheeger constant and by the exponential volume growth of distance balls. (C) 2016 Elsevier Ltd. All rights reserved.
Author details: | Matthias Keller, Delio Mugnolo |
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DOI: | https://doi.org/10.1016/j.na.2016.07.011 |
ISSN: | 0362-546X |
ISSN: | 1873-5215 |
Title of parent work (English): | Theoretical ecology |
Publisher: | Elsevier |
Place of publishing: | Oxford |
Publication type: | Article |
Language: | English |
Year of first publication: | 2016 |
Publication year: | 2016 |
Release date: | 2020/03/22 |
Tag: | Cheeger inequalities; Intrinsic metrics for Dirichlet forms; Spectral theory of graphs |
Volume: | 147 |
Number of pages: | 16 |
First page: | 80 |
Last Page: | 95 |
Funding institution: | Land Baden-Wurttemberg; DFG |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
Peer review: | Referiert |