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Analysis and Geometry in Metric Spaces

Ed. by Ritoré, Manuel

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Distance Bounds for Graphs with Some Negative Bakry-Émery Curvature

Shiping Liu
  • Corresponding author
  • School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, Anhui Province, China
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/ Florentin Münch / Norbert Peyerimhoff / Christian Rose
Published Online: 2019-03-22 | DOI: https://doi.org/10.1515/agms-2019-0001


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.

Keywords: Bakry-Émery curvature; discrete Bonnet-Myers theorem; intrinsic metric; heat semigroup

MSC 2010: Primary: 51K10; Secondary: 51F99, 05C12


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About the article

Received: 2018-04-02

Accepted: 2019-01-29

Published Online: 2019-03-22

Published in Print: 2019-03-01

Citation Information: Analysis and Geometry in Metric Spaces, Volume 7, Issue 1, Pages 1–14, ISSN (Online) 2299-3274, DOI: https://doi.org/10.1515/agms-2019-0001.

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© 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

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