The Ricci flow on a cylinder

TL;DR

This paper investigates the Ricci flow on cylindrical surfaces, establishing long-term existence, analyzing asymptotic behavior, and revealing that convergence to constant curvature may not be exponential under certain initial conditions.

Contribution

It provides new results on the long-time behavior of Ricci flow on cylinders and highlights a phenomenon regarding the non-exponential convergence to constant curvature.

Findings

Longtime existence of Ricci flow on cylindrical surfaces

Asymptotic analysis of flow behavior

Convergence to constant curvature may not be exponential

Abstract

In this paper we study the Ricci flow on surfaces homeomorphic to a cylinder (that is, a product of the circle with a compact interval). We prove longtime existence results, results on the asymptotic behavior of the flow, and we report on an interesting phenomenon: convergence to constant curvature in the normalised flow,under certain assumptions on the initial data, cannot be exponential.