Uniformity of harmonic map heat flow at infinite time

Details Uniformity of harmonic map heat flow at infinite time Uniformity of harmonic map heat flow at infinite time

2012-02-26

arxiv.org/abs/1202.5756v1

Mathematics

Differential Geometry

19 pages

Scientific paper

We show an energy convexity along any harmonic map heat flow with small initial energy and fixed boundary data on the unit 2-disk. In particular, this gives an affirmative answer to a question raised by W. Minicozzi asking whether such 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.

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