Abstract
The main goal in this paper is to report the asymptotic expansion of Green's function of the conformal Laplacian on a compact Riemannian manifold without boundary. First of all, we introduce the conformal normal coordinates. Second, we discuss the expansion of Green's function in the conformal normal coordinates. Finally, we give some application in section 4. This report is based on the lecture note by R. Schoen and S.-T. Yau and the paper by J. M. Lee and T. H. Parker.