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

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

2004-04-22

arxiv.org/abs/math/0404415v1

Ann. of Math. (2), Vol. 158 (2003), no. 1, 323--343

Mathematics

Differential Geometry

21 pages, published version

Scientific paper

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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