The Case of a Bounded Number of Vortices

Abstract

In this chapter, we prove upper bound and lower bound estimates for configurations with a number of vortices bounded as ε → 0 which reduces to considering a number of vortices independent of ε. These estimates will be useful in the next chapter. The fact that the number of vortices is bounded independently of ε allows us to obtain much more precise information with specific techniques: the upper and lower bounds will match up to an error which is o(1) as ε → 0.