×

Uniformity of harmonic map heat flow at infinite time. (English) Zbl 1294.53062

Summary: 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.

MSC:

53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010)
58E20 Harmonic maps, etc.
PDF BibTeX XML Cite
Full Text: DOI arXiv

References:

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.