Vol. 6, No. 8, 2013

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Uniformity of harmonic map heat flow at infinite time

Longzhi Lin

Vol. 6 (2013), No. 8, 1899–1921

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 W1,2-topology, as time goes to infinity, to the unique limiting harmonic map.

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harmonic map heat flow, energy convexity, uniform convergence
Mathematical Subject Classification 2010
Primary: 53C44, 58E20
Received: 23 July 2012
Accepted: 22 August 2013
Published: 20 April 2014
Longzhi Lin
Department of Mathematics
Rutgers University
110 Frelinghuysen Road
Piscataway, New Jersey 08854-8019
United States