Scalar curvatures on S 2. (English) Zbl 0635.35026

Chen, Wenxiong; Ding, Weiyue

Trans. Am. Math. Soc. 303, 365-382 (1987).

The authors prove a theorem for the existence of a solution of the nonlinear elliptic equation \(-\Delta u+2=R(x)\ell\) 4, \(u\in S\) 2 under some conditions on R(x) but not symmetry. This is the first existence result where R(x) is not symmetric. The proof of the existence uses a mass center analysis technique and a continuous flow in H 1(S 2) controlled by \(\nabla R\).

Reviewer: C.F.Wang

MSC:

35J60	Nonlinear elliptic equations
35J20	Variational methods for second-order elliptic equations
53C99	Global differential geometry

Keywords:

existence; mass center; flow