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Vers une théorie des points critiques à l’infini. (Towards a theory of critical points at infinity). (French) Zbl 0585.58004
Sémin. Bony-Sjöstrand-Meyer, Équations Dériv. Partielles 1984-1985, Exp. No. 8, 23 p. (1985).
Let E be a Hilbert manifold and \(f: E\to {\mathbb{R}}^ a\) \(C^ 2\)- functional. The object of the calculus of variations is to find and study critical points of the functional f, i.e. points \(x\in E\) with \(\partial f(x)=0\) (\(\partial f\) being the gradient of f). An important tool are compactness conditions like the Palais-Smale condition. In many problems this is not available. One has to study the deformations along the gradient flows directly. The authors do this for the Yamabe equations, the Kazdan-Warner problem and contact structures. [See also the following review.]
Reviewer: G.Warnecke

58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
53C20 Global Riemannian geometry, including pinching
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