$Q$-Curvature and Poincaré Metrics
By Charles Fefferman, C. Graham. 2001
205 citations recorded by the source corpus.
This article presents a new definition of Branson's Q-curvature in even-dimensional conformal geometry. We derive the Q-curvature as a coefficient in the asymptotic expansion of the formal solution of a boundary problem at infinity for the Laplacian in the Poincare metric associated to the conformal structure. This gives an easy proof of the result of Graham-Zworski that the log coefficient in the volume expansion of a Poincare metric is a multiple of the integral of the Q-curvature, and leads to a definition of a non-local version of the Q-curvature in odd dimensions.
Subfields: Applied Mathematics, Geometry and Topology, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/442c60efce3480433cfd8d75696ea4f0cfb8f705
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- A. Malchiodi
- Z. Djadli
- C. B. Ndiaye
- Thomas Leistner
- Daniele Bartolucci
- Jun-cheng Wei
- Alessandro Carlotto
- Yanyan Li
In Geometry and Topology
In Nuclear and High Energy Physics
Citations in the corpus
- Conformal holonomy of C-spaces, Ricci-flat, and Lorentzian manifolds (2005, methodology): “The idea of using an ambient metric in order to describe conformal structures goes back to C. Fefferman and C. Robin Graham [FG85], for recent results see [ FG02 ], [ y Cap02] [FH03], [ y”
- Existence of conformal metrics with constant Q-curvature (2004, background): “Finally, we also point out that the Paneitz operator and the Q-curvature (together with their higher-dimensional analogues, see [5], [6], [26], [27]) appear in the study of Moser-Trudinger type inequalities, log-determinant formulas and the compactification of locally conformally flat manifolds, [7]”
- Fractional conformal Laplacians and fractional Yamabe problems (2010, unknown): “[27], [19]).”