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We prove universal recursive formulas for Branson's $Q$-curvatures in terms of respective lower-order $Q$-curvatures, lower-order GJMS-operators and holographic coefficients.
C. R. Graham, Extended obstruction tensors and renormalized volume coefficients, Adv. Math
1985
Earlier work this paper cites.
C. R. Graham, R. Jenne, L. J. Mason and G. A. J. Sparling. Conformally invariant powers of the Laplacian. I. Existence. J. London Math. Soc. (2)
1992
Earlier work this paper cites.
T. Branson, Sharp inequalities, the functional determinant, and the complementary series. Trans. Amer. Math. Soc
1995
Earlier work this paper cites.
C. R. Graham, Volume and area renormalizations for conformally compact Einstein metrics, Rend. Circ. Mat. Palermo (2) Suppl
2000
Earlier work this paper cites.
A. R. Gover and L. Peterson. Conformally invariant powers of the Laplacian, Q Q -curvature, and tractor calculus. Comm. Math. Phys
2003
Cited alongside, same era.
C. R. Graham and M. Zworski, Scattering matrix in conformal geometry, Invent. Math
2003
Cited alongside, same era.
C. R. Graham and A. Juhl, Holographic formula for Q Q -curvature, Adv. Math
2007
Cited alongside, same era.
A. Juhl, Families of Conformally Covariant Differential Operators, Q Q -Curvature and Holography
2009
Cited alongside, same era.
C. Fefferman and C. R. Graham. The ambient metric. arXiv:0710.0919v2
Cited in the paper.
A. Juhl, On conformally covariant powers of the Laplacian. arXiv:0905.3992v3
Cited in the paper.
Cited in the paper.
A. Juhl, Explicit formulas for GJMS-operators and Q Q -curvatures, (in preparation)
Cited in the paper.
H. Baum and A. Juhl, Conformal Differential Geometry: Q Q -curvature and Conformal Holonomy
2010
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A. Juhl, On Branson’s Q Q -curvature of order eight. Conformal Geometry and Dynamics
2011
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A. Juhl, Holographic formula for Q Q -curvature. II. Adv. in Math
2011
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