The long time behavior of fourth-order curvature flows

Details The long time behavior of fourth-order curvature flows The long time behavior of fourth-order curvature flows

2011-03-21

arxiv.org/abs/1103.4136v2

Mathematics

Differential Geometry

Final version, to appear in Calc. Var. PDE

Scientific paper

We show precompactness results for solutions to parabolic fourth order geometric evolution equations. As part of the proof we obtain smoothing estimates for these flows in the presence of a curvature bound, an improvement on prior results which also require a Sobolev constant bound. As consequences of these results we show that for any solution with a finite time singularity, the $L^{\infty}$ norm of the curvature must go to infinity. Furthermore, we characterize the behavior at infinity of solutions with bounded curvature.

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