Distance Bounds for Graphs with Some Negative Bakry-Émery Curvature

Liu, Shiping; Münch, Florentin; Peyerimhoff, Norbert; Rose, Christian

doi:10.1515/agms-2019-0001

Distance Bounds for Graphs with Some Negative Bakry-Émery Curvature

Liu, Shiping; Münch, Florentin; Peyerimhoff, Norbert; Rose, Christian

Authors

Shiping Liu

Florentin Münch

Professor Norbert Peyerimhoff norbert.peyerimhoff@durham.ac.uk
Professor

Christian Rose

Abstract

We prove distance bounds for graphs possessing positive Bakry-Émery curvature apart from an exceptional set, where the curvature is allowed to be non-positive. If the set of non-positively curved vertices is finite, then the graph admits an explicit upper bound for the diameter. Otherwise, the graph is a subset of the tubular neighborhood with an explicit radius around the non-positively curved vertices. Those results seem to be the first assuming non-constant Bakry-Émery curvature assumptions on graphs.

Citation

Liu, S., Münch, F., Peyerimhoff, N., & Rose, C. (2019). Distance Bounds for Graphs with Some Negative Bakry-Émery Curvature. Analysis and Geometry in Metric Spaces, 7(1), 1-14. https://doi.org/10.1515/agms-2019-0001

Journal Article Type	Article
Acceptance Date	Jan 29, 2019
Online Publication Date	Mar 22, 2019
Publication Date	Mar 31, 2019
Deposit Date	Apr 11, 2019
Publicly Available Date	Apr 11, 2019
Journal	Analysis and Geometry in Metric Spaces
Publisher	De Gruyter Open
Peer Reviewed	Peer Reviewed
Volume	7
Issue	1
Pages	1-14
DOI	https://doi.org/10.1515/agms-2019-0001

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Copyright Statement
© 2019 Shiping Liu et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 Public License. BY 4.0