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The gradient flow of the $L^2$ curvature energy on surfaces (1008.4311v1)
Published 25 Aug 2010 in math.DG and math.AP
Abstract: We investigate the gradient flow of the $L2$ norm of the Riemannian curvature on surfaces. We show long time existence with arbitrary initial data, and exponential convergence of the volume normalized flow to a constant scalar curvature metric when the initial energy is below a constant determined by the Euler characteristic of the underlying surface.
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