Annals of Global Analysis and Geometry

, Volume 28, Issue 1, pp 19–34 | Cite as

The Problem of Prescribed Critical Functions

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Abstract

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 constants Sobolev inequalities 

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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

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