# A note about the strong maximum principle on $RCD$ spaces

## TL;DR

This paper provides a straightforward proof of the strong maximum principle in finite dimensional RCD spaces, utilizing Laplacian comparison of the squared distance to establish the result.

## Contribution

It offers a new, direct proof of the strong maximum principle specifically tailored for finite dimensional RCD spaces.

## Key findings

- Proof based on Laplacian comparison of squared distance
- Simplifies the understanding of maximum principles in RCD spaces
- Enhances the theoretical framework of geometric analysis on metric measure spaces

## Abstract

We give a quick and direct proof of the strong maximum principle on finite dimensional $RCD$ spaces based on the Laplacian comparison of the squared distance.