# The Ricci curvature on simplicial complexes

## TL;DR

This paper introduces a new way to define Ricci curvature on simplicial complexes, extending graph-based concepts, and uses it to estimate Laplacian eigenvalues, broadening geometric analysis tools.

## Contribution

It generalizes Ricci curvature to simplicial complexes and establishes bounds and eigenvalue estimates, advancing geometric analysis in higher-dimensional structures.

## Key findings

- Defined Ricci curvature on simplicial complexes.
- Proved bounds for Ricci curvature in this setting.
- Estimated Laplacian eigenvalues using the new curvature.

## 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.