A note on scalar curvature type problems in dimension 4 |
| |
Authors: | Ezequiel R Barbosa Marcos Montenegro |
| |
Institution: | Departamento de Matemática, Universidade Federal de Minas Gerais, Caixa Postal 702, 30161-970 Belo Horizonte, MG, Brazil |
| |
Abstract: | Let (M,g) be a 4-dimensional compact Riemannian manifold and let a,f be positive smooth functions on M. In this note, we prove that the problem Δgu+a(x)u=f(x)u3 always admits a positive solution, up to a conformal deformation of g. This leads to a geometric obstruction result for the prescribed scalar curvature problem. |
| |
Keywords: | Prescribed scalar curvature problem Geometric obstruction |
本文献已被 ScienceDirect 等数据库收录! |
|