Q-curvature prescription; forbidden functions and the GJMS null space

Gover, A.

doi:10.1090/S0002-9939-09-10111-9

Q-curvature prescription; forbidden functions and the GJMS null space
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by A. Rod Gover PDF

Proc. Amer. Math. Soc. 138 (2010), 1453-1459 Request permission

Abstract:

On a closed even conformal manifold $(M,c)$, such that the critical GJMS operator has a non-trivial kernel, we identify and discuss the role of a finite dimensional vector space $\mathcal {N}(\mathcal {Q})$ of functions determined by the conformal structure. Using these we describe an infinite dimensional class of functions that cannot be the Q-curvature $Q^g$ for any $g\in c$. If certain functions arise in $\mathcal N(\mathcal Q)$, then $Q^g$ cannot be constant for any $g\in c$.

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