Variational Aspects of the Seiberg-Witten Functional

Details Variational Aspects of the Seiberg-Witten Functional Variational Aspects of the Seiberg-Witten Functional

1995-04-28

arxiv.org/abs/dg-ga/9504003v1

Mathematics

Differential Geometry

14 pages, AMS-tex

Scientific paper

The Seiberg-Witten equations that have recently found important applications for four-dimensional geometry are the Euler-Lagrange equations for a functional involving a connection $A$ on a line bundle $L$ and a section $\phi$ of another bundle $W^+$ constructed from $L$ and a spinor bundle on a given four-dimensional Riemannian manifold. We show the regularity of weak solutions and the Palais-Smale condition for this functional.

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