On Branson's $Q$-curvature of order eight

Abstract

We prove a universal recursive formulas for Branson's $Q$-curvature of order eight in terms of lower-order $Q$-curvatures, lower-order GJMS-operators and holographic coefficients. The results prove a special case of a conjecture in {arXiv:0905.3992}.

25 pages

References in corpus (5)

• On conformally covariant powers of the Laplacian
• Holographic formula for Q-curvature
• Conformally invariant powers of the Laplacian -- A complete non-existence theorem
• Extended obstruction tensors and renormalized volume coefficients
• Summation formulas for GJMS-operators and Q-curvatures on the Möbius sphere