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

2004/04/22 by Simon Brendle · 1 citation
Mathematics · #math.DG

paper · pdf

published as Ann. of Math. (2), Vol. 158 (2003), no. 1, 323--343 · 21 pages, published version

arxiv created 2004/04/22 · arxiv updated 2009/12/01

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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