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arXiv · 1909.06422

Uniqueness and nonuniqueness of limits of Teichmueller harmonic map flow

James Kohout·Melanie Rupflin·Peter M. Topping
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Abstract

The 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 time tends to infinity.

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James Kohout, Melanie Rupflin, Peter M. Topping. 2019-09-13. Uniqueness and nonuniqueness of limits of Teichmueller harmonic map flow. https://arxiv.org/abs/1909.06422

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