# Ricci curvature in dimension 2

## TL;DR

This paper proves that in two-dimensional spaces, the synthetic definitions of lower bounds on sectional and Ricci curvature are equivalent, clarifying their relationship in this specific setting.

## Contribution

The paper establishes the equivalence of synthetic lower bounds for sectional and Ricci curvature in two-dimensional spaces, a previously unclear relationship.

## Key findings

- Sectional and Ricci curvature bounds coincide in 2D
- Synthetic curvature notions are equivalent in 2D
- Clarifies curvature bounds relationship in low dimensions

## Abstract

We prove that in two dimensions the synthetic notions of lower bounds on sectional and on Ricci curvature coincide.