Convergence of the Yamabe flow for arbitrary initial energy

We consider the Yamabe flow ∂g ∂t = −(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.

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