Global regularity of wave maps IV. Absence of stationary or self-similar solutions in the energy class

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Tao, Terence
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Using the harmonic map heat flow, we construct an energy class for wave maps $\phi$ from two-dimensional Minkowski space $\R^{1+2}$ to hyperbolic spaces $\H^m$, and then show (conditionally on a large data well-posedness claim for such wave maps) that no stationary, travelling, self-similar, or degenerate wave maps exist in this energy class. These results form three of the five claims required in our earlier paper (arXiv:0805.4666) to prove global regularity for such wave maps. (The conditional claim of large data well-posedness is one of the remaining claims required in that paper.)
Comment: 77 pages, no figures. Will not be published in current form, pending future reorganisation of the heatwave project
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Mathematics - Analysis of PDEs, 35L70
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