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 x ∈ M such that f(x) > 0.
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Mathematics Subject Classifications (2000): 53C21, 46E35, 26D10.
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Humbert, E., Vaugon, M. The Problem of Prescribed Critical Functions. Ann Glob Anal Geom 28, 19–34 (2005). https://doi.org/10.1007/s10455-005-1583-8
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DOI: https://doi.org/10.1007/s10455-005-1583-8