Annals of Global Analysis and Geometry

, Volume 28, Issue 1, pp 19–34

The Problem of Prescribed Critical Functions


DOI: 10.1007/s10455-005-1583-8

Cite this article as:
Humbert, E. & Vaugon, M. Ann Glob Anal Geom (2005) 28: 19. doi:10.1007/s10455-005-1583-8


Let (M,g) be a compact Riemannian manifold on dimension n ≥ 4 not conformally diffeomorphic to the sphere Sn. 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 constantsSobolev inequalities

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Institut Élie CartanUniversité de Nancy 1Vandoeuvre-Lès-Nancy CedexFrance
  2. 2.Institut de mathématiques de JussieuUniversité de Paris 6ParisFrance