Uniqueness and nonuniqueness of limits of Teichmüller harmonic map flow
Keyword(s):
AbstractThe harmonic map energy of a map from a closed, constant-curvature surface to a closed target manifold can be seen as a functional on the space of maps and domain metrics. We consider the gradient flow for this energy. In the absence of singularities, previous theory established that the flow converges to a branched minimal immersion, but only at a sequence of times converging to infinity, and only after pulling back by a sequence of diffeomorphisms. In this paper, we investigate whether it is necessary to pull back by these diffeomorphisms, and whether the convergence is uniform as {t\to\infty}.
2005 ◽
Vol 39
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pp. 781-796
2019 ◽
Vol 55
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pp. 1011-1041
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2019 ◽
Vol 63
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pp. 155-166
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2004 ◽
Vol 159
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pp. 465-534
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2013 ◽
Vol 50
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pp. 883-924
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1995 ◽
Vol 3
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pp. 95-105
2019 ◽
Vol 39
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pp. 6913-6943