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


Author: A. Rod Gover
Journal: Proc. Amer. Math. Soc. 138 (2010), 1453-1459
MSC (2010): Primary 53A30; Secondary 35J60, 53A55
DOI: https://doi.org/10.1090/S0002-9939-09-10111-9
Published electronically: December 11, 2009
MathSciNet review: 2578539
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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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Additional Information

A. Rod Gover
Affiliation: Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland 1142, New Zealand
Email: gover@math.auckland.ac.nz

DOI: https://doi.org/10.1090/S0002-9939-09-10111-9
Keywords: Q-curvature, curvature prescription, conformal differential geometry
Received by editor(s): October 28, 2008
Received by editor(s) in revised form: June 10, 2009
Published electronically: December 11, 2009
Communicated by: Matthew J. Gursky
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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