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

Let B-2 subset of R-2 and S-2 subset of R-3 be the unit disk and the unit sphere, and let v: B-2 x R+ --> S-2 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. (C) 2003 Elsevier Science (USA). All rights reserved.