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

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

2010-08-25

arxiv.org/abs/1008.4311v1

Mathematics

Differential Geometry

Scientific paper

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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