## Scalar curvatures on S 2.(English)Zbl 0635.35026

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
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