A quantization property for static Ginzburg-Landau vortices

For any critical point of the complex Ginzburg-Landau functional in dimensi on 3, we prove that, for large coupling constants, kappa = 1/epsilon; if th e energy of this critical point on a ball of a given radius r is relatively small compared to r log r/epsilon, then the ball of half-radius contains n o vortex (the modulus of the solution is larger than 1/2). We then show how this property can be applied to describe limiting vortices as epsilon --> 0. (C) 2001 John Wiley & Sons, Inc.