The scalar-curvature problem on the standard three-dimensional sphere. (English) Zbl 0722.53032

The authors study the problem of finding a metric conformally equivalent to the standard metric on the sphere \(S^ 3\) and with prescribed scalar curvature K. The difficulty consists in the failure of the Palais-Smale condition of the corresponding variational problem. This difficulty is overcome in the paper under certain (non-degeneracy) assumptions on K.
Reviewer: W.Ballmann (Bonn)


53C20 Global Riemannian geometry, including pinching
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