Strict type-II blowup in harmonic map flow

Abstract

A finite-time singularity of 2D harmonic map flow will be called “strictly type-II” if the outer energy scale satisfies λ ( t ) = O ( T − t ) 1 + α 2 . \begin{equation*} \lambda (t) = O (T-t)^{\frac {1 + \alpha }{2} }. \end{equation*} We prove that the body map at a strict type-II blowup is Hölder continuous. This is relevant to a conjecture of Topping.