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.

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.