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The Palais–Smale conditions for the Yang–Mills functional

Published online by Cambridge University Press:  14 November 2011

D. R. Wilkins
D. R. Wilkins
Affiliation:
Department of Pure Mathematics, Trinity College, Dublin 2, Republic of Ireland
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Synopsis

We consider the Yang–Mills functional denned on connections on a principal bundle over a compact Riemannian manifold of dimension 2 or 3. It is shown that if we consider the Yang–Mills functional as being defined on an appropriate Hilbert manifold of orbits of connections under the action of the group of principal bundle automorphisms, then the functional satisfies the Palais–Smale condition.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 108 , Issue 3-4 , 1988 , pp. 189 - 200
Copyright
Copyright © Royal Society of Edinburgh 1988

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