The gradient flow of the $L^2$ curvature energy on surfaces

Jeffrey Streets

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arXiv · 1008.4311

The gradient flow of the $L^2$ curvature energy on surfaces

Jeffrey Streets

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Abstract

We investigate the gradient flow of the $L^2$ 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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Jeffrey Streets. 2010-08-25. The gradient flow of the $L^2$ curvature energy on surfaces. https://arxiv.org/abs/1008.4311

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