Mathematische Zeitschrift

, Volume 247, Issue 2, pp 279–302

Winding behaviour of finite-time singularities of the harmonic map heat flow*

  • Peter Topping

DOI: 10.1007/s00209-003-0582-3

Cite this article as:
Topping, P. Math. Z. (2004) 247: 279. doi:10.1007/s00209-003-0582-3


We settle a number of questions about the possible behaviour of the harmonic map heat flow at finite-time singularities. In particular, we show that a type of nonuniqueness of bubbles can occur at finite time, we show that the weak limit of the flow at the singular time can be discontinuous, we determine exactly the (polynomial) rate of blow-up in one particular example, and we show that ‘winding’ behaviour of the flow can lead to an unexpected failure of convergence when the flow is (locally) lifted to the universal cover of the target manifold.

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Peter Topping
    • 1
  1. 1.Mathematics InstituteUniversity of WarwickCoventryUK