$Q$-Curvature and Poincaré Metrics

@article{Fefferman2001QCurvatureAP,
  title={\$Q\$-Curvature and Poincar{\'e} Metrics},
  author={Charles Fefferman and C. Robin Graham},
  journal={Mathematical Research Letters},
  year={2001},
  volume={9},
  pages={139-151}
}
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… Expand
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