×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI