Explicit formulas for GJMSoperators and $Q$curvatures
Abstract
We describe GJMSoperators as linear combinations of compositions of natural secondorder differential operators. These are defined in terms of PoincaréEinstein metrics and renormalized volume coefficients. As special cases, we find explicit formulas for conformally covariant third and fourth powers of the Laplacian. Moreover, we prove related formulas for all Branson's $Q$curvatures. The results settle and refine conjectural statements in earlier works. The proofs rest on the theory of residue families.
 Publication:

arXiv eprints
 Pub Date:
 August 2011
 arXiv:
 arXiv:1108.0273
 Bibcode:
 2011arXiv1108.0273J
 Keywords:

 Mathematics  Differential Geometry;
 High Energy Physics  Theory;
 Mathematical Physics;
 05A19;
 35J30;
 53A30;
 53B20 (Primary) 35Q76;
 53A55;
 53C25;
 58J50 (Secondary)
 EPrint:
 84 pages, revised argument in proof of Theorem 3.1, corrected typos