On the nonexistence of finite time bubble trees in symmetric harmonic map heat flows from the disk to the 2-sphere

Abstract

Let B2⊂R2 and S2⊂R3 be the unit disk and the unit sphere, and let v:B2×R+→S2 be a radially symmetric harmonic map heat flow, whose singularities coincide with downward energy jumps. Then its finite time singularities are simple in the sense that precisely one harmonic sphere separates at a time.