, Volume 28, Issue 1, pp 19-34

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 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.

Mathematics Subject Classifications (2000): 53C21, 46E35, 26D10.