×

On Coleman’s principle for finding the stationary points of quadratic functionals. (English. Russian original) Zbl 0537.49025

Sov. Math., Dokl. 27, 624-627 (1983); translation from Dokl. Akad. Nauk SSSR 270, 529-532 (1983).
The authors show that the principle ”an extremum of f on \(X_ 0\) is an extremum of f on X” is not valid in general if we suppose that X is a manifold, G is a group acting on X, f is an invariant functional on X and \(X_ 0\) is the set of all fixed points of X. They find those conditions on X, G and f under which the principle is valid and apply it to a problem of Skyrme and to the Higgs model.
Reviewer: S.Balint

MSC:

49Q20 Variational problems in a geometric measure-theoretic setting
46A19 Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than \(\mathbb{R}\), etc.)
58E15 Variational problems concerning extremal problems in several variables; Yang-Mills functionals
55M20 Fixed points and coincidences in algebraic topology
PDFBibTeX XMLCite