Existence and stability of shrinkers for the harmonic map heat flow in higher dimensions

We study singularity formation for the heat flow of harmonic maps from Rᵈ R d . For each d ≥ 4 d ≥ 4 , we construct a compact, d -dimensional, rotationally symmetric target manifold that allows for the existence of a corotational self-similar shrinking solution (shortly shrinker ) that represents a stable blowup mechanism for the corresponding Cauchy problem.