A relative entropy and a unique continuation result for Ricci expanders

TL;DR

This paper establishes an optimal convergence rate and a unique continuation property at infinity for Ricci expanders, and introduces a well-defined relative entropy for these self-similar solutions.

Contribution

It provides the first optimal convergence rate and a unique continuation result at infinity for Ricci expanders, along with defining a relative entropy for these solutions.

Findings

Proves an optimal relative integral convergence rate for Ricci expanders.

Establishes a unique continuation result at infinity for Ricci expanders.

Defines a well-behaved relative entropy for self-similar Ricci flow solutions.

Abstract

We prove an optimal relative integral convergence rate for two expanding gradient Ricci solitons coming out of the same cone. As a consequence, we obtain a unique continuation result at infinity and we prove that a relative entropy for two such self-similar solutions to the Ricci flow is well-defined.