# The Canonical Expanding Soliton and Harnack inequalities for Ricci flow

## TL;DR

This paper introduces Canonical Expanding Ricci Solitons to derive new Harnack inequalities for Ricci flow, providing geometric insights and extending previous inequalities by Hamilton and Brendle.

## Contribution

The paper presents a novel concept of Canonical Expanding Ricci Soliton and uses it to establish new Harnack inequalities with geometric interpretations.

## Key findings

- Derived new Harnack inequalities for Ricci flow
- Provided geometric insights into existing inequalities
- Extended the framework of Ricci solitons

## Abstract

We introduce the notion of Canonical Expanding Ricci Soliton, and use it to derive new Harnack inequalities for Ricci flow. This viewpoint also gives geometric insight into the existing Harnack inequalities of Hamilton and Brendle.