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

TL;DR

This paper derives recursive formulas for Branson's eighth-order Q-curvature, connecting it to lower-order curvatures and operators, confirming a specific conjecture in the field.

Contribution

It provides the first explicit recursive formulas for eighth-order Q-curvature, advancing understanding of higher-order conformal invariants.

Findings

Recursive formulas for eighth-order Q-curvature derived

Confirmed a special case of a conjecture from prior work

Links between Q-curvature, GJMS-operators, and holographic coefficients established

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}.