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Q-Curvature and Poincare Metrics

Charles Fefferman·C. Robin Graham
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Abstract

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.

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Charles Fefferman, C. Robin Graham. 2001-10-24. Q-Curvature and Poincare Metrics. https://arxiv.org/abs/math/0110271

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