an:04190611
Zbl 0722.53032
Bahri, Abbas; Coron, Jean-Michel
The scalar-curvature problem on the standard three-dimensional sphere
EN
J. Funct. Anal. 95, No. 1, 106-172 (1991).
00156256
1991
j
53C20
conformal change of the metric; standard sphere; prescribed scalar curvature
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.
W.Ballmann (Bonn)