TL;DR
This paper explores the applications of Ricci flow in physics, including its role in renormalization group flow, Ricci solitons, mass flow in higher dimensions, and potential implications in general relativity.
Contribution
It reviews existing applications of Ricci flow in physics and presents recent results on mass flow in higher dimensions and its possible relevance to general relativity.
Findings
Ricci flow arises in nonlinear sigma models' RG flow
Ricci solitons are used to analyze mass flow in 2D
New results on mass flow in higher dimensions
Abstract
I discuss certain applications of the Ricci flow in physics. I first review how it arises in the renormalization group (RG) flow of a nonlinear sigma model. I then review the concept of a Ricci soliton and recall how a soliton was used to discuss the RG flow of mass in 2-dimensions. I then present recent results obtained with Oliynyk on the flow of mass in higher dimensions. The final section discusses one way in which Ricci flow may arise in general relativity, particularly for static metrics.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.