Bakry-Emery curvature and diameter bounds on graphs
- We prove finiteness and diameter bounds for graphs having a positive Ricci-curvature bound in the Bakry–Émery sense. Our first result using only curvature and maximal vertex degree is sharp in the case of hypercubes. The second result depends on an additional dimension bound, but is independent of the vertex degree. In particular, the second result is the first Bonnet–Myers type theorem for unbounded graph Laplacians. Moreover, our results improve diameter bounds from Fathi and Shu (Bernoulli 24(1):672–698, 2018) and Horn et al. (J für die reine und angewandte Mathematik (Crelle’s J), 2017, https://doi.org/10.1515/crelle-2017-0038) and solve a conjecture from Cushing et al. (Bakry–Émery curvature functions of graphs, 2016).
| Author details: | Shiping LiuORCiD, Florentin MünchGND, Norbert Peyerimhoff |
|---|---|
| DOI: | https://doi.org/10.1007/s00526-018-1334-x |
| ISSN: | 0944-2669 |
| ISSN: | 1432-0835 |
| Title of parent work (English): | Calculus of variations and partial differential equations |
| Publisher: | Springer |
| Place of publishing: | Heidelberg |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2018/03/15 |
| Publication year: | 2018 |
| Release date: | 2021/12/17 |
| Volume: | 57 |
| Issue: | 2 |
| Number of pages: | 9 |
| Funding institution: | EPSRCEngineering & Physical Sciences Research Council (EPSRC) [EP/K016687/1]; German Research Foundation (DFG)German Research Foundation (DFG) |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Peer review: | Referiert |
| Publishing method: | Open Access / Green Open-Access |
