Quantitative uniqueness and vortex degree estimates for solutions of the Ginzburg-Landau equation

In this paper, we provide a sharp upper bound for the maximal order of vanishing for non-minimizing solutions of the Ginzburg-Landau equation $$ Delta u=-{1overepsilon^2}(1-|u|^2)u $$ which improves our previous result cite{Ku2}. An application of this result is a sharp upper bound for the degree of any vortex. We treat Dirichlet (homogeneous and non-homogeneous) as well as Neumann boundary conditions.