Repulsion and quantization in almost-harmonic maps, and asymptotics of the harmonic map flow


We present an analysis of bounded-energy low-tension maps between 2-spheres. By deriving sharp estimates for the ratio of length scales on which bubbles of opposite orientation develop, we show that we can establish a ‘quantization estimate’ which constrains the energy of the map to lie near to a discrete energy spectrum. One application is to the asymptotics of the harmonic map flow; we find uniform exponential convergence in time, in the case under consideration.


Peter Topping

Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom