The Logarithmic Singularities of the Green Functions of the Conformal Powers of the Laplacian

@article{Ponge2013TheLS,
title={The Logarithmic Singularities of the Green Functions of the Conformal Powers of the Laplacian},
author={Raphael Ponge},
journal={arXiv: Differential Geometry},
year={2013}
}

Green functions play an important role in conformal geometry. In this paper, we explain how to compute explicitly the logarithmic singularities of the Green functions of the conformal powers of the Laplacian. These operators include the Yamabe and Paneitz operators, as well as the conformal fractional powers of the Laplacian arising from scattering theory for Poincar\'e-Einstein metrics. The results are formulated in terms of Weyl conformal invariants arising from the ambient metric of… CONTINUE READING