Convergence of the yamabe flow for arbitrary initial energy

Abstract

We consider the Yamabe flow ∂g/∂t = ȡ(Rg − rg)g, where g is a Riemannian metric on a compact manifold M, Rg denotes its scalar curvature, and rg denotes the mean value of the scalar curvature. We prove convergence of the Yamabe flow if the dimension n satisfies 3 ≤ n ≤ 5 or the initial metric is locally conformally flat. © 2005 Applied Probability Trust.