In this chapter we show that the vortex balls provided by Theorem 4.1, although they are constructed through a complicated process and are not completely intrinsic to (u,A) (and not unique), have in the end a simple relation to the configuration (u,A), namely that the measure Σi2πdiδai is close in a certain norm to the gauge-invariant version of the Jacobian determinant of u, an intrinsic quantity depending on (u,A). This will allow us, in the next chapters, to extract from Gε(u,A), in addition to the vortex energy πΣi |di||log ε| contained in the vortex balls, a term describing vortex-vortex interactions and vortex-applied field interactions in terms of the measure Σi2πdiδai.


Lipschitz Function Radon Measure Universal Constant Continuous Bounded Function Jacobian Determinant 
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© Birkhäuser Boston 2007

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