Ricci flow on Riemannian groupoids

TL;DR

This paper investigates the Ricci flow on Riemannian groupoids with compact, connected orbit spaces, establishing short-term existence, uniqueness, and introducing a F-functional for steady breathers.

Contribution

It extends Ricci flow theory to Riemannian groupoids, proving fundamental existence and uniqueness results and defining a new F-functional for steady breathers.

Findings

Proved short time existence of Ricci flow on Riemannian groupoids.

Established uniqueness of the Ricci flow in this setting.

Defined a F-functional and analyzed steady breathers.

Abstract

We study the Ricci flow on Riemannian groupoids. We assume that these groupoids are closed and that the space of orbits is compact and connected. We prove the short time existence and uniqueness of the Ricci flow on these groupoids. We also define a F-functional and derive the corresponding results for steady breathers on these spaces.