The Ricci Curvature on Simplicial Complexes

Authors

Taiki Yamada, Shimane UniversityFollow

Publication Date

December 2023

Abstract

We define the Ricci curvature on simplicial complexes modifying the definition of the Ricci curvature on graphs, and prove upper and lower bounds of the Ricci curvature. These properties are generalizations of previous studies. Moreover, we obtain an estimate of the eigenvalues of the Laplacian on simplicial complexes by the Ricci curvature.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

Recommended Citation

Yamada, Taiki (2023) "The Ricci Curvature on Simplicial Complexes," Theory and Applications of Graphs: Vol. 10: Iss. 2, Article 5.
DOI: 10.20429/tag.2023.10205
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol10/iss2/5