Uniformity of harmonic map heat flow at infinite time
Differential Geometry
2018-06-18 v1 Analysis of PDEs
Abstract
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.
Keywords
Cite
@article{arxiv.1202.5756,
title = {Uniformity of harmonic map heat flow at infinite time},
author = {Longzhi Lin},
journal= {arXiv preprint arXiv:1202.5756},
year = {2018}
}
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19 pages