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.

71p tuanloccuoi 04-01-2013 73 7   Download