A topological hypothesis for the prescribed scalar curvature problem. (Une hypothèse topologique pour le problème de la courbure scalaire prescrite.) (French) Zbl 0916.58041

Aubin, T.; Bahri, A.

J. Math. Pures Appl., IX. Sér. 76, No. 10, 843-850 (1997).

For a given compact manifold \((V^n,g)\), \(n\geq 3\), the authors consider the problem which functions are the scalar curvature of a metric conformal to \(g\). Extending their results in [T. Aubin and A. Bahri, J. Math. Pures Appl., IX. Ser. 76, No. 6, 525-549 (1997; Zbl 0886.58109)] they show for a class of functions satisfying certain analytical and topological properties how to solve this so-called prescribed scalar curvature problem. As an application of their result, they give an example of a function on a torus which up to now couldn’t be seen to be such a curvature function.

Reviewer: Barbara Priwitzer (Tübingen)

MSC:

58J05	Elliptic equations on manifolds, general theory
53C21	Methods of global Riemannian geometry, including PDE methods; curvature restrictions
35J60	Nonlinear elliptic equations

Keywords:

conformal metric; prescribed scalar curvature

Citations:

Zbl 0886.58109

References:

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