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Global existence and convergence for a higher order flow in conformal geometry

Simon Brendle
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Abstract

We study a higher-order parabolic equation which generalizes the Ricci flow on two-dimensional surfaces. The metric is deformed conformally with a speed given by the Q-curvature of the metric. Under a condition on the Q-curvature of the initial metric we show that the soluton exists for all time and converges to a metric of prescribed Q-curvature.

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Simon Brendle. 2004-04-22. Global existence and convergence for a higher order flow in conformal geometry. https://arxiv.org/abs/math/0404415

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