Nonexistence of finite-time blow-up for the equivariant harmonic map heat flow from $B^2$ to $S^2$

Abstract

We consider $D$-equivariant solutions to the harmonic map heat flow from $B^2$ to $S^2$ under general time-dependent smooth boundary data and prove that there is no finite-time blow-up when $D\ge 2$.

Result was improved from D $\ge 3$ to $D\ge 2$. Several mistakes in the proof were also fixed