Explicit formulas for GJMS-operators and $Q$-curvatures
Differential Geometry
2022-03-28 v4 High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
We describe GJMS-operators as linear combinations of compositions of natural second-order differential operators. These are defined in terms of Poincar\'e-Einstein 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 -curvatures. The results settle and refine conjectural statements in earlier works. The proofs rest on the theory of residue families.
Cite
@article{arxiv.1108.0273,
title = {Explicit formulas for GJMS-operators and $Q$-curvatures},
author = {Andreas Juhl},
journal= {arXiv preprint arXiv:1108.0273},
year = {2022}
}
Comments
84 pages, revised argument in proof of Theorem 3.1, corrected typos