Full blow-up range for co-rotaional wave maps to surfaces of revolution

We construct blow-up solutions of the energy critical wave map equation on $\mathbb{R}^{2+1}\to \mathcal N$ with polynomial blow-up rate ($t^{-1-ν}$ for blow-up at $t=0$) in the case when $\mathcal{N}$ is a surface of revolution. Here we extend the blow-up range found by Cârstea ($ν>\frac 12$) based on the work by Krieger, Schlag and Tataru to $ν>0$. This work relies on and generalizes the recent result of Krieger and the author where the target manifold is chosen as the standard sphere.

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