Elliptic Problems in the Study of Selfdual Vortex Configurations
The examples of selfdual problems discussed in the previous chapter all share a common equation (see (2.1.1) below), which can be viewed as a gauge-invariant version of the Cauchy–Riemann equation.
Following an approach introduced by Taubes (cf. [JT]), we see next how to use such a property in order to eliminate the gauge invariance from the selfdual equations and formulate them in terms of elliptic problems of the Liouville-type, whose analysis will be the main objective of our study.
KeywordsElliptic Problem Liouville Equation Vortex Point Cartan Matrix Vortex Solution
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