The gradient flow of the L² curvature energy on surfaces

2010/08/25 by Streets, Jeffrey
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1008.4311

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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