# Uniformity of harmonic map heat flow at infinite time

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Longzhi Lin, Rutgers University
Fine Hall 314

We will discuss an energy convexity along the harmonic map heat flow with small initial energy and fixed boundary data on the unit 2-disk. In particular, this shows that such weak harmonic map heat flow converges uniformly in time strongly in the W^{1,2}-topology, as time goes to infinity, to the unique limiting harmonic map.