Q-curvature prescription; forbidden functions and the GJMS null space
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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 $g\in c$.References
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Additional Information
- A. Rod Gover
- Affiliation: Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland 1142, New Zealand
- MR Author ID: 335695
- Email: gover@math.auckland.ac.nz
- 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
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2578539