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2013 Uniformity of harmonic map heat flow at infinite time
Longzhi Lin
Anal. PDE 6(8): 1899-1921 (2013). DOI: 10.2140/apde.2013.6.1899

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

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Longzhi Lin. "Uniformity of harmonic map heat flow at infinite time." Anal. PDE 6 (8) 1899 - 1921, 2013. https://doi.org/10.2140/apde.2013.6.1899

Information

Received: 23 July 2012; Accepted: 22 August 2013; Published: 2013
First available in Project Euclid: 20 December 2017

zbMATH: 1294.53062
MathSciNet: MR3198587
Digital Object Identifier: 10.2140/apde.2013.6.1899

Subjects:
Primary: 53C44 , 58E20

Keywords: energy convexity , harmonic map heat flow , Uniform convergence

Rights: Copyright © 2013 Mathematical Sciences Publishers

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Vol.6 • No. 8 • 2013
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