Annals of Global Analysis and Geometry

, Volume 28, Issue 1, pp 19-34

First online:

The Problem of Prescribed Critical Functions

  • Emmanuel HumbertAffiliated withInstitut Élie Cartan, Université de Nancy 1 Email author 
  • , Michel VaugonAffiliated withInstitut de mathématiques de Jussieu, Université de Paris 6

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Let (M,g) be a compact Riemannian manifold on dimension n ≥ 4 not conformally diffeomorphic to the sphere S n . We prove that a smooth function f on M is a critical function for a metric g conformal to g if and only if there exists xM such that f(x) > 0.

Key words

best constants Sobolev inequalities