The Ricci curvature on simplicial complexes
Spectral Theory
2022-06-06 v4 Differential Geometry
Abstract
We define the Ricci curvature on simplicial complexes by modifying the definition of the Ricci curvature on graphs, and we prove the 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 using the Ricci curvature.
Cite
@article{arxiv.1906.07404,
title = {The Ricci curvature on simplicial complexes},
author = {Taiki Yamada},
journal= {arXiv preprint arXiv:1906.07404},
year = {2022}
}
Comments
13 pages