Q-Curvature and Poincare Metrics

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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.
13 pages

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Differential Geometry

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http://salesiana.dossiersoluciones.com/handle/123456789/62485

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0110271
 http://arxiv.org/abs/math/0110271

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arXiv