Open Access
Feb 2005 Convergence of the Yamabe flow for arbitrary initial energy
Simon Brendle
J. Differential Geom. 69(2): 217-278 (Feb 2005). DOI: 10.4310/jdg/1121449107


We consider the Yamabe flow $\frac{\partial g}{\partial t} = -(R_g - r_g) \, g$ where $g$is a Riemannian metric on a compact manifold $M, R_g$ denotes its scalar curvature, and $r_g$ denotes the mean value of the scalar curvature. We prove convergence of the Yamabe flow if the dimension $n$ satisfies $3 \leq n \leq 5$ or the initial metric is locally conformally flat.


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Simon Brendle. "Convergence of the Yamabe flow for arbitrary initial energy." J. Differential Geom. 69 (2) 217 - 278, Feb 2005.


Published: Feb 2005
First available in Project Euclid: 15 July 2005

zbMATH: 1085.53028
MathSciNet: MR2168505
Digital Object Identifier: 10.4310/jdg/1121449107

Rights: Copyright © 2005 Lehigh University

Vol.69 • No. 2 • Feb 2005
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