The gradient flow of the $L^2$ curvature energy near the round sphere

Details The gradient flow of the $L^2$ curvature energy near the round sphere The gradient flow of the $L^2$ curvature energy near the round sphere

2010-03-08

arxiv.org/abs/1003.1707v1

Mathematics

Differential Geometry

Scientific paper

We investigate the low-energy behavior of the gradient flow of the $L^2$ norm
of the Riemannian curvature on four-manifolds. Specifically, we show long time
existence and exponential convergence to a metric of constant sectional
curvature when the initial metric has positive Yamabe constant and small
initial energy.

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